Given: [tex]cosec[/tex] [tex]A[/tex] [tex]=\sqrt{2}[/tex]
∴ [tex]A=\frac{\pi }{4} =45^{0}[/tex]
[tex]sin[/tex] [tex]A[/tex] [tex]=sin[/tex] [tex]45^{0}[/tex] = [tex]\frac{1}\sqrt{2}[/tex]
[tex]cot[/tex] [tex]A[/tex] [tex]=cot[/tex] [tex]45^{0}[/tex] [tex]=1,[/tex]
[tex]tan[/tex] [tex]A[/tex] [tex]=[/tex] [tex]tan[/tex] [tex]45^{0}[/tex] [tex]=1[/tex]
[tex]cos[/tex] [tex]A[/tex] [tex]=[/tex] [tex]cot[/tex] [tex]45^{0}[/tex] [tex]=\frac{1}{\sqrt{2} }[/tex]
∴ [tex]=2[/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
METHOD 1: Using Trigonometric values.
We have given that,
[tex]\sf\cosec\theta=\sqrt2[/tex]
So,
[tex]\sf\theta=45^{\circ}[/tex]
We need to find:
[tex]\sf\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+\sin^2(45^{\circ})+\cos^2(45^{\circ})}{1+\sec^2(45^{\circ})-\tan^2(45^{\circ})}[/tex]
[tex]\sf\longmapsto\dfrac{1+\left(\frac{1}{\sqrt2}\right)^2+\left(\frac{1}{\sqrt2}\right)^2}{1+(\sqrt2)^2-(1)^2}[/tex]
[tex]\sf\longmapsto\dfrac{1+\frac{1}{2}+\frac{1}{2}}{1+2-1}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{2}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
METHOD 2: Using Trigonometric Identities
We need to find:
[tex]\implies\dfrac{1+\sin^2\theta+\cos^2\theta}{1+\sec^2\theta-\tan^2\theta}[/tex]
But, we know that,
[tex]\sf\red⇛ \sin^2\phi+\cos^2\phi=1[/tex]
And,
[tex]\sf\red⇛ \sec^2\phi-\tan^2\phi=1[/tex]
So,
[tex]\sf\longmapsto\dfrac{1+(\sin^2\theta+\cos^2\theta)}{1+(\sec^2\theta-\tan^2\theta)}[/tex]
[tex]\sf\longmapsto\dfrac{1+1}{1+1}[/tex]
[tex]\sf\longmapsto\dfrac{2}{2}[/tex]
[tex]\sf\longmapsto\bf1[/tex]
Therefore, by both methods the answer is 1.
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Similar questions
Prove that:
\cos( \frac{3\pi}{2} + \theta) \cos(2\pi + \theta) [ \cot( \frac{3\pi}{2} - \theta) + \cot(2\pi + \theta) ] = 1...
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Plz help. Thank youuu
Answer:
c
Step-by-step explanation:
cause
For what value of c is the function one-to-one?
StartSet (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c) EndSet
2
5
11
13
Answer:
13
Step-by-step explanation:
Correct on edge
The function will be one-to-one only if c = 13.
When a function is one-to-one?
A function is one-to-one if and only if each value in the range appears only once.
So, the given set will represent a one-to-one function if c takes a value that is not repeated in any of the other coordinate pairs.
We have:
(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
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how do you write y - 2 = -(x - 3) in slope-intercept form? A) y = x + 3 B) y = x - 1 C) y = -x + 5 D) y = -3x - 1
Help pleaseeeeeeeeeeeeeeeeeeeeeee
Answer:
I have to say this problem is poorly worded.
the answer they're looking for is 8, I believe.
they defined t(x) twice!
Find the slope of the line that passes through each pair of points. Expressed as a fraction in simplest form. (8,2),(8,-1)
Answer:
x = 8
Step-by-step explanation:
The explanation are the pictures. I hope I gave you the correct answer.
-0.6-3.1=? Fine each difference
Answer:
-3.7
Step-by-step explanation:
i think this is right if you meant to say find instead of fine
Find the slope of each line.
Answer:
The slope is m=1, y=1x-2
Step-by-step explanation:
Therefore, the slope is 1/1 so 1.
what is this problem please help70^1/3
Answer:
23.333....
Step-by-step explanation:
May I please receive help?
Can someone help me with part b?
Step-by-step explanation:
the average rate of change of a function f in an interval [x-low, x-high] is
(f(x-high) - f(x-low)) / (x-high - x-low)
the year 2000 means t = 2000-1980 = 20
the year 2015 means t = 2015-1980 = 35
so, we have
(A(35) - A(20)) / (35 - 20)
((-0.6(35)² + 37.2×35 + 243) - (-0.6(20)² + 37.2×20 + 243)) / 15
((-735 + 1302 + 243) - (-240 + 744 + 243)) / 15
(810 - 747) / 15 = 63/15 = 4.2
the average change rate between 2000 and 2015 is 4.2.
that means that the use of nuclear energy in the USA increased by 4.2 billions of kilowatt hours per year during that period.
hi Help pls will mark as brainlist!!!!!!!!!
Answer:
111
Step-by-step explanation:
the answer is c)111
hop it helps
how can 1/5 + (-4/5) be modeled on a number line ? complete the sentance. then move 4/5 in the ? direction
Answer:
negative direction
Step-by-step explanation:
A negative and a positive make a negative:
1/5 + (-4/5) = 1/5 - 4/5
Hope this helps!
Which of the following could possibly be
used to describe the number of people
wearing braces in this room?
A. Whole Numbers
B. Negative Numbers
C. Rational Numbers
D. Irrational Numbers
Answer:
Hi I believe A. whole numbers
plz let me know if im right
Can some pls help me?
Answer:
4
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
E to A is 3 and D to A is 2 so you add the two together and get 5 which is B.
Let me know if I'm wrong.
4-1/4 with no decimal point
Answer:
4-25
Step-by-step explanation:
Helppppppp pleaseee tyy smmm
Answer: 56
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
what is the answer?
Answer:
(write this in the format your curriculum suggests, most are different)
Since BC is longer than AB, this means m<bcd is smaller than m<bad.
A way to prove it mathematically is to look at the triangle on the left. Since It's an isosceles triangle, m<cda and m<dac are equal. However, the triangle on the right does not have two proven congruent sides. All we know is BC is larger than the other side lengths. In a figure like that, the obtuse angle that meets the longest side would be the largest angle.
Apologies for being so wordy.
PLS HELP RIGHT NOW !!!!
Answer:
1-*8364464737353=kgkdtyry
please help I dont understand
Answer:
Step-by-step explanation:
Find the slope between (9 , 75) and (13 , 95)
-4 = 20 - 10x
i dont know what to do pls help
Answer:
x = 2.4
Step-by-step explanation:
10x = 24
x = 24 ÷ 10
x = 2.4
Step-by-step explanation:
→ -4 = 20 - 10x
→ -20 - 4 = 10x
→ -24 = 10x
→ x = -24/10
→ x = -2.4
therefore, value of x is -2.4
hope this answer helps you dear!
ALL FELLOW PEOPLE I NEED HELP ASAP ! WILL MARK BRAINLIEST!!EXTRA POINTS !!!!
Answer:
3) parallel
4) y = -1/2x +5
Step-by-step explanation:
3) Two equations are parallel if they have the same slope
The equations are written in y=mx+b (standard) form, where m is the slope. Both equations have a slope of 5/4
4) The two points that are plotted are (0,5) and (4,3).
We can find the slope by using the slope equation
(3) - (5) / (4) - (0) = -2/4 = -1/2
then we can plug it in both points to find b
-1/2(4) = -2
-2 + b = 3
b = 3
Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
Question 3 options:
AB=RS
AB=2RS
ΔABC~ΔRST
△ABC≅ΔRST
m∠BAC=m∠SRT
m∠BAC=2m∠SRT
The given reflection transformation is a rigid transformation, such that the dimensions are preserved
The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;
AB = RSΔABC ≅ ΔRSTm∠BAC ≅ m∠SRTReasons:
The given parameters are;
Triangle ΔABC is reflected across the line y = 2·x
Given that a reflection is a rigid transformation, we have;
The distance between two points on a preimage is the same as the distance between the corresponding points on the image;
Therefore;
ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;
AB ≅ RS, BC ≅ ST, and AC ≅ RT
m∠BAC ≅ m∠SRT
m∠BCA ≅ m∠STR
m∠BAC ≅ m∠SRT
Therefore;
The true statements are;
AB = RSΔABC ≅ ΔRSTTherefore;
m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRSTLearn more here:
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Solve for the value of c.
Step-by-step explanation:
(8c-5)°=(6c-3)°
8c°-5°=6c°-3°
8c°-6c°=-3°-5°
2c°=-8°
c°=-8/2
c°= -4
Substitute the value
{8(-4)-5}
-32-5
-37°
(6c-3)
{6(-4)-3}
-24-3
-27
Newton’s Second Law of Motion states that the acceleration of an object is directly proportional to the force exerted on the object. If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2 ?
Answer:35N
Step-by-step explanation:
Cross multiply and divide to find the missing value
What is the value of x
Explain why the triangle are similar. Then find the distance represented by x
Answer:
I think its the rule RHS or SAS that indicates that x is 180ft (scale factor of 1.5)
Step-by-step explanation:
first do 135/90 to find the scale factor of 1.5
then to find x, multiply 120 by the scale factor.
NEED help asap please find the percentage
Hope this helps, have a nice day!!
What can be described as “shooting stars” that streak across the sky in a brief flash of light?(1 point)
comets
meteors
meteoroids
meteorites
Answer:
the answers for the quick check:
Step-by-step explanation:
1. d. spiral
2. b stars
3. d. meteors
4. d. as it gets closer to the sun
“Shooting Stars” that streak across the sky in a brief flash of light is Option b) Meteors.
"Shooting stars" are captivating phenomena seen in the night sky. They are commonly mistaken for stars, but they are not stars at all.
Shooting stars, or meteors, are not celestial bodies themselves, but rather the luminous trails created when small space rocks, known as meteoroids, enter Earth's atmosphere at high speeds.
These meteoroids are remnants from comets or asteroids.
When a meteoroid collides with Earth's atmosphere, friction causes it to heat up rapidly.
This intense heat causes the meteoroid to vaporize in a brilliant flash of light, leaving behind a streak across the sky.
This streak is what we commonly refer to as a shooting star or meteor.
Comets, denoted by option (a), are icy bodies that originate from the outer regions of the solar system.
They can produce meteoroids, which in turn create meteors when they enter Earth's atmosphere. However, comets themselves are not what we see as shooting stars.
Meteoroids, as mentioned in option (c), are the actual rocky or metallic fragments that create meteors.
When a meteoroid survives its fiery passage through the atmosphere and lands on Earth's surface, it is referred to as a meteorite, as stated in option (d).
In summary, shooting stars, or meteors, are the dazzling result of meteoroids burning up as they speed through Earth's atmosphere. This captivating display is a reminder of the continuous cosmic activity surrounding our planet, turning the night sky into a canvas of transient and awe-inspiring light shows.
To know more about Meteors here
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#SPJ3
NOTE: This not a Question of Mathematics, this is a Question from Physics
Complete Question
Choose the correct answer from the given options:
What can be described as “shooting stars” that streak across the sky in a brief flash of light?
a) Comets
b) Meteors
c) Meteoroids
d) Meteorites
a helicopter flies over a city the helicopter changes it's altitude by -42.9m. then it changes it's altitude by another -15.4m what is the total change in the helicopters altitude
Answer:
The total change in the helicopter's altitude is [tex]-58.3[/tex].
Step-by-step explanation:
Create an equation.
[tex]-42.9 +(-15.4)[/tex]
Adding two negative numbers is always negative, so simply add the absolute values and make the answer a negative.
[tex]42.9+15.4 = 58.3[/tex]
Now, change the answer to a negative.
[tex]-58.3[/tex]
Thus, [tex]-58.3[/tex] is the answer.
What value of x satisfies the equation 5(x – 3) – 2(x + 1) = 4?
Answer:
x = 7
Step-by-step explanation:
To solve:
Distribute 5 among everything inside the first parentheses. You'll get 5x - 15.
Next distribute -2 among everything in the second parentheses. You'll get
-2x - 2.
All together: 5x - 15 -2x - 2 = 4
Now combine like terms:
5x - 2x = 3x and -15 - 2 = - 17
All together: 3x - 17 = 4
Add 17 on both sides to get 21, and then divide both sides by 3. Answer is x = 7.
________________________________
Last, don't forget to check your work.
You can plug in 7 for x to get:
5(7 - 3) = 20
5 × 7 = 35
5 × -3 = -15
35 - 15 = 20
-2(7 + 1) = -16
-2 × 7 = -14
-2 × 1 = - 2
-14 -2 = -16
20 - 16 = 4
⬆⬆⬆Therefore this is correct.
Sorry this is a bit lengthy, but hope this helps :)