Prove that:
[tex] \cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1 [/tex]
Please solve this problem because tomorrow is my maths exam.​

Answers

Answer 1

Explanation:

On taking LHS

Cos[(3π/2)+θ]Cos(2π+θ)[Cot{(3π/2)-θ}+Cot(2π+θ)]

We know that

π = 180°

2π = 2×180° = 360°

3π/2 = (3×180°)/2 = 540°/2 = 270°

Now

LHS becomes

Cos(270°+θ)Cos(360°+θ)[Cot(270°-θ)+Cot(360°+θ)]

We know that

Cos (270°+θ) = Sin θ

Cos (360°+θ) = Cos θ

Cot (270°-θ) = Tan θ

Cot (360°+θ) = Cot θ

→ Sin θ Cos θ [Tan θ + Cot θ]

→ Sinθ Cosθ[(Sinθ/Cosθ)+(Cosθ/Sinθ)]

→ Sinθ Cosθ[(Sin²θ+Cos²θ)/(SinθCosθ)]

→ Sin θ Cos θ [1/(Sin θ Cos θ)]

Since Sin²θ+Cos²θ = 1

→ (Sin θ Cos θ)/(Sin θ Cos θ)

→ 1

→ RHS

→ LHS = RHS

Hence, Proved.

Here are the formulae that I have used:

→ π = 180°

→ Cos (270°+θ) = Sin θ

→ Cos (360°+θ) = Cos θ

→ Cot (270°-θ) = Tan θ

→ Cot (360°+θ) = Cot θ

Here are the Trigonometric Identities that I have used:

→ Sin²θ+Cos²θ = 1


Related Questions

950.3 divided by 37 were doing partial product divison

Answers

I think it’s 25.6 or not

[tex]10\times 5\times 13=?[/tex]

Answers

Answer:

[tex] = > 10 \times 5 \times 13[/tex]

[tex] = > 50 \times 13[/tex]

[tex] = > 650[/tex]

Yash can buy three pencils and have 49c change, or he can buy five pencils and
have 15c change.
(1) Write this information as an equation for x the cost in cents of one pencil.
(ii) How much money did Yash have to start with?

Answers

Answer:

(ii) 1 dollar

Step-by-step explanation:

each pencil costs 17 cents

- thus 3 pencils x 17c is 51c

1.00 dollars minus 0.51 is 49

- 5 pencils x 17c is equal to 85

1.00 dollars minus 0.85 is 15 c

Write the standard form of 7384000000​

Answers

Answer:To write a linear expression in standard form, rearrange the terms in alphabetical order.

7384000000

Step-by-step explanation:

Answer:

738400000.0

Step-by-step explanation:

738400000.0*10^10

Quis
Jika
A= 2
B= 3
D=2
maka
A x B ÷C​

Answers

Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

Answer:

A= 2

B= 3

D=2

maka

A x B ÷C

2 x 3 ÷ 2

=6 ÷ 2

=3

pls help..........!!!!!!

Answers

Answer:

1) 1085 ÷ 7

7 )1085(155

- 7

38

- 35

× 35

- 35

0

1085 ÷ 7 = 155

2) 7104 ÷ 32

32 )7104(222

- 64

× 70

- 64

×64

- 64

××

7104 ÷ 32 = 222

3) 2244 ÷ 51

51)2244(44

- 204

×244

- 244

×××

2244 ÷ 51 = 33

4) 1584 ÷ 12

12)1584(132

- 12

×38

- 36

×24

- 24

××

1584 ÷ 12 = 132

5) 1467 ÷ 9

9)1467(163

- 9

56

- 54

27

- 27

××

1467 ÷ 9 = 163

6) 2830 ÷ 28

28)2830(101

- 28

××3

- 0

30

- 28

×2

2830 ÷ 28 = 101 with the remainder 2

7) 9090 ÷ 45

45)9090(202

- 90

××9

- 0

90

- 90

××

9090 ÷ 45 = 202

8) 7000 ÷ 62

62)7000(112

- 62

×80

- 62

180

- 125

×55

7000 ÷ 62 = 112 with the remainder 55

9) 1150 ÷ 15

15)1150(76

- 105

×100

- 90

10

1150 ÷ 15 = 76 with the remainder 10

Hope that my answer is right and helpful to you

I need answer immediately!!!!!!

Answers

Its division and fractions i advise calulater soup

can someone help please? u dont have to show work so dont mind that

Answers

Answer:

Factor the numerator and denominator and cancel the common factors.

x/4+3/2 or 32/4  or Reduce the expression, if possible, by cancelling the common factors. 8 is your final answer

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

First, you substitute.

x + 6 / 4

26 + 6 / 4

Then, you add.

26 + 6 = 32

Finally, you divide.

32 / 4 = 8

Answer: 8

What is the value of h(3)?

–2
–1
1
2

Answers

Answer:

C) 1

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

Step-by-step explanation:

h(3) means that x = 3. That's the right side of the x axis. At that point, h(3) has a y value of 1.



Solve the system of equations using the substitution method.
x+y=6
x = 2y


Answers

y=2

if you substitute 2y in for x, you get 2y+1y=6. that is also 3y=6. 6 divided by 3 is 2 so y=2.

Answer:

x=4, y=2

Step-by-step explanation:

if x=2y just put 2y into the spot where x is for x+y=6

x+y=6

(2y) + y = 6

3y = 6

y = 2

now that I know y I can then replace y with the number 2

x= 2y

x = 2(2)

x= 4

Can someone please help me with this?

Find the x- and y-intercepts of the equation.
4x − 2y = 2

(A) (1/2,0). (0,1)
(B). (2, 0), (0, −1)
(C). (2, 0), (0, −1)
(D). (1/2, 0), (0, −1)

Answers

Answer:

Option D

Step-by-step explanation:

Convert to slope-intercept form:

[tex]4x-2y=2[/tex]

[tex]-2y=2-4x[/tex]

[tex]y=-1+2x[/tex]

[tex]y=2x-1[/tex]

Find the x-intercept by plugging in y=0:

[tex]y=2x-1[/tex]

[tex]0=2x-1[/tex]

[tex]1=2x[/tex]

[tex]\frac{1}{2}=x[/tex]

[tex]x=\frac{1}{2}[/tex]

Therefore, the x-intercept is [tex](\frac{1}{2},0)[/tex]

Find the y-intercept by plugging in x=0:

[tex]y=2x-1[/tex]

[tex]y=2(0)-1[/tex]

[tex]y=0-1[/tex]

[tex]y=-1[/tex]

Therefore, the y-intercept is [tex](0,-1)[/tex]

So, the correct answer is option D.

Answer:

D

Step-by-step explanation:

1. To find the x intercepts, set y equal to 0 and solve for x

4x - 2y = 2

4x -2(0) = 2

4x - 0 = 2

4x = 2

x = 1/2

2. To find the y intercepts, set x equal to 0 and solve for y

4x - 2y = 2

4(0) - 2y = 2

0 - 2y = 2

-2y = 2

y = -1

The slope and y intercept

Answers

Answer:

the y intercept is 5 because the line passes through 5 on the y axis. Now to find the slope, pick two points where the line hits directly on the corner of the grid squares. pIck 2 of those and count the squares up till you are lined up with your other point then count over and get another number. Put the number going up over the number going down like x/y and you'll have your answer. ( simplify it if you can.(-2,3) and (0,5) are a good place to start. The answer should be 2/3. Hope this helped and God bless!

can someone check these for me? lmk if they are wrong and how to correct them please

Answers

Answer:

the 1. is y = (5/4)x + 6 and 2 . is y = 20x+10, so you are right, both of them correct

Matt's pool table is 3 feet wide and 9 feet long. Matt wants to replace the felt on the pool table. The felt costs $4.00 per square foot. How much would it cost in total to replace the felt on the pool table?

Answers

Answer:

$108

Step-by-step explanation:

3X9= 27square foot. Then you multiply 27 by 4, which equals $108

writing carla has already written 10 pages of a novel she plans to write 15 additional pages per month until she is finished A.write an equation to find the total number of pages P written after any number of months MB. graph the equation on the grid at the rightC. find the total number of pages written after 5 months

Answers

Answer:

P = 5M + 10

Step-by-step explanation:

15 pages/month * M months + 10 pages = P pages

5 Months = 5*15 + 10 = 85 pages

Express the values below I’m scientific notation 52,800g, 255.6m, 0.04109cm!?

Answers

Answer:

1) 5.28 x 10^4 g

2)2.556 x 10^2 m

3)4.109 × 10^-2cm

Have a nice day!!!!!

Answer:

52,800 in scientific notation is [tex]5.28[/tex] × [tex]10^4[/tex].

255.6 in scientific notation is [tex]2.556[/tex] × [tex]10^2[/tex].

0.04109 in scientific notation is [tex]4.109[/tex] × [tex]10^{-2}[/tex].

PLEASE HELP ME WITH GEOMETRY 15 POINTS

Answers

X=15 because you divide 2 on both sides and get x and 15

subtract (3x^3-2x+5)-(-4x^3+3x-6)

Answers

Answer:

7x^3-5x+11

Step-by-step explanation:

(3x^3-2x+5)-(-4x^3+3x-6)

Distribute

3x^3-2x+5+4x^3-3x+6

Simplify

7x^3-5x+11

3x³-2x+5-(-4x³+3x-6)3x³-2x+5+4x³-3x+63x³+4x³-2x-3x+5+67x³-5x+11

These are two similar triangles
What is the measure of x?
24
12
X
4
x = [?]
=

Answers

I believe the answer should be 18. Try

literally can no one help, i said id give brainliest and anything u need, i jst want all of it answered

Answers

A) She received the discount during January but not February.

B) $94.98

C) The equation is 394.94 = 59.99x + 34.99y, where x is the number of months she had membership and visited less than 12 times, and y it’s the number of months she had membership while going 12 or more times.

A cylindrical glass has a radius of 4 centimetres and a height of 6 centimetres. A. large cylindrical jar full of water is a similar shape to the glass. The glass can be filled with water from the jar exactly 216 times. Work out the radius and height of the jar.

Please answer correctly with explanation :-)​

Answers

Step-by-step explanation:

follow the above attachment.

hope this helps you.

helppppppppppppppppppppppppppppppppppppppppppp sorry for that

Answers

Answer:

a)2 * 2 = 4

b)2 * 3/2 = 3

c) 20 * 3/2 = 30

d) 100 * 8/5 = 160

e)473*1/100=4.73

f)111*1/100=1.11

Answer:

answers are written

Step-by-step explanation:

2xx671.0

Solve the simultaneous equations
x-6y=5
xy - 2y2 = 6
-
Show clear algebraic working.

Answers

Answer:

(- 7, - 2 ) , (9.5, 0.75 )

Step-by-step explanation:

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y = [tex]\frac{3}{4}[/tex] = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

(- 7, - 2 ) and  (9.5, 0.75 ) are the solutions.

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here, we have,

Given the equations

x - 6y = 5 ( add 6y to both sides )

x = 5 + 6y → (1)

xy - 2y² = 6 → (2)

Substitute x = 5 + 6y into (2)

(5 + 6y)y - 2y² = 6 ← distribute and rearrange left side

5y + 6y² - 2y² = 6

4y² + 5y = 6 ( subtract 6 from both sides )

4y² + 5y - 6 = 0 ← in standard form

(y + 2)(4y - 3) = 0 ← in factored form

Equate each factor to zero and solve for y

y + 2 = 0 ⇒ y = - 2

4y - 3 = 0 ⇒ 4y = 3 ⇒ y =  = 0.75

Substitute these values into (1) for corresponding values of x

y = - 2 : x = 5 + 6(- 2) = 5 - 12 = - 7 ⇒ (- 7, - 2 )

y = 0.75 : x = 5 + 6(0.75) = 5 + 4.5 = 9.5 ⇒ (9.5, 0.75 )

To learn more on equation click:

brainly.com/question/24169758

#SPJ2

help me please.

Rounding questions.

Answers

Step-by-step explanation:

a) 6400

b) 4800

c) 32000

hope this answer helps you dear!

PLEASE HELP WILL MARK BRAINLIEST NO RANDOM ANSWERS

Answers

-6y + 4 + 6y -4 + 2
=2

Hello salvadorbea340!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex] - (6y - 4) + (6y - 4) - ( - 2)[/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex]-(6y-4)+(6y-4)-(-2)[/tex]

Firstly, let's open the brackets of the 1st term, i.e. - (6y - 4).

[tex] -( 6y - 4) \\ = \underline{\underline{- 6y + 4}}[/tex]

Now, the 2nd term [ (6y - 4) ].

[tex] + ( 6y - 4) \\ = \underline{\underline{ + 6y - 4}}[/tex]

Now, the 3rd term ⇨ - (- 2)

[tex] -( - 2) \\ = \underline{\underline{ + 2}}[/tex]

Now, let's bring the equation together.

[tex]- (6y - 4) + (6y - 4) - ( - 2) \\ = - 6y + 4 + 6y - 4 + 2[/tex]

Now, let's solve the equation.

Firstly, bring the like terms together.

[tex]- 6y + 4 + 6y - 4 + 2 \\ = - 6y + 6y + 4 - 4 + 2[/tex]

Now cancel out -6y & +6y and 4 & -4 as they make 0.

[tex]- 6y + 6y + 4 - 4 + 2 \\ = \bcancel{- 6y }+ \bcancel{6y} + \bcancel{ \: \: 4 } \: \: - \bcancel{ \: 4 }+ 2 \\ = 0 + 2 \\ = 2[/tex]

And, the only number left is 2. So our answer is 2.

[tex] = \large\boxed{\boxed{ 2}}[/tex]

__________________

Hope it'll help you!

ℓu¢αzz ッ

Evaluate -(2")(2º).
A.1/8
B. -8
C. 8
D.-1/8

Answers

Answer:

= -8

(hope this helps) :)

If x=√7/5 and 5/x=p√7 find p
Plz tell fast
I will mark as branliest

Thank you

Answers

Replace x with √7/5

5/√7/5 = p √7

Divide both sides by √7

P = 5/√7/5 /√7

P = 25/7

Answer: p = 25/7

What is another name for an ordered subset?
A. Probability
B. Combination
C. Permutation​

Answers

Answer: b

Step-by-step explanation:

can somebody please just help me do not answer if you do not know

Answers

Answer:

it could be 34 , 34 and 82

or 34 , 73 and 37

Step-by-step explanation:

angles in a triangle add up to 180. in and isosceles triangle two angles are always the same so there will be 2 possible outcomes.

pls mark brainalist

At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.40 and the cost of a large greeting card is $3.70. How much would it cost to get 2 small greeting cards and 3 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?

Answers

Answer:

1)15.9

depends on what x and y are but put 15.9 ig

Step-by-step explanation:

Answer:

cost of smalls + cost of larges so the answer is 2.40+3.70

Step-by-step explanation:

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