how to solve the attachment question?

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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Answer:

A is right answer

Step-by-step explanation:

because - - = +

Answer:

its the lastone

Step-by-step explanation:

Answer:

answer for 10th question is 121

Step-by-step explanation:

2(a+b)+a+b/2+(a+b)^2-4

=2(10)+10/2+(10)^2-4

=20+5+100-4

=125-4

=121

Answer:

10.  121      11.  Hamburger = $1.43

Step-by-step explanation:

2(a + b) + (a + b)/2 + (a + b)² - 4

2(10) + (10)/2 + (10)² - 4

20 + 5 + 100 - 4

25 + 100 - 4

125 - 4 = 121

11.   Let H = Hamburger and Soft Drink = D

          H + D = $2.23

      2 H + 3D = $5.26

H + D = $2.23        Solve for D

D = $2.23 - H        

2H + 3D = $5.26     Now substitute the value of H into the second equation.

2H + 3($ 2.23 - H) = $5.26

2H + $6.69 - 3H = $5.26

 -H + $6.69 = $5.26

 -H = - $1.43

  H = $1.43

we need to subtract

[tex]\\ \sf\longmapsto 300251-21596[/tex]

[tex]\\ \sf\longmapsto 278655[/tex]

Now let's round up

[tex]\\ \sf\longmapsto 278700[/tex]

[tex]\\ \sf\longmapsto 279000[/tex]

[tex]\\ \sf\longmapsto 280000[/tex]

[tex]\\ \bf\longmapsto 300000[/tex]

Answer:

33

Step-by-step explanation:

if its in () its the 1th step and then the rest u can continue

Answer:

C. The product of 12 and √17

Step-by-step explanation:

Because it gives a number that isn't a repeating or terminating decimal.

Answer:

What subject is this

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Answer:

-24

Step-by-step explanation:

Answer:-24

Step-by-step explanation:if its the same sign u just add and keep the sign.

Answer:  The Van needs 18 gallons of gas to travel 360 miles.

Answer:

Step-by-step explanation:

y = 4.8x + C

53.8 = 4.8(4) + C

53.8 = 19.2 + C

C = 34.6

Answer:

(-7, -7)

Step-by-step explanation:

1. Let's ONLY focus on point C.

2. The algebraic rule for reflecting across the y-axis is (x, y) -> (-x, y).

3. The algebraic rule for translating 8 units down is (x, y) -> (x, y - 8).

Therefore, the coordinates for C' are (-7, -7).

Answer: 10h+ 4

Step-by-

Answer:

y ≤ 20-8x

Step-by-step explanation:

Darren needs to spend no more than 15 hours on cardio exercise (y). To figure out how much time he has we need to do 20-8x. Any leftover hours are the hours left for him to spend doing his exercises. Since y has to be less than or equal to 20-8x, the system of linear inequalities should be:

y ≤ 20-8x

Answer:

25.)Yesss

26.)Yesss she have enough money to buy a popcorn and soda

27.)?

Step-by-step explanation:

#Hopeee it Helpssss

follow me pls.

Answer:

The circumference is the distance around a circle. In other words, it's the perimeter of the circle. And we find the circumference by using the formula C = 2πr.

Step-by-step explanation:

Answer:

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Answer:

35

Step-by-step explanation:

70 minutes for 24 songs

70/2 minutes for 24/2 songs

35 minutes for 12 songs.

Answer:

35 minutes for 12 songs

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:in the picture

Answer:x=[tex]\frac{13}{2}[/tex] or x= 6.5 either way x equals to the number 6.5 .

Step-by-step explanation:The image below will explain how you solve the problem also thanks for the person above me for the idea of answering this question.

HOPE THIS HELPS

:)

Also website as seen in the photo is symbolab

Answer:

17

Step-by-step explanation:

Answer:

A {5, 10, 15, 20}

Step-by-step explanation:

Answer:

27/7

the mixed number 3 6/7 can be written as 27/7.

The value of an improper fraction in the lowest term is,

⇒ 27/7

We have to give that,

A mixed fraction is,

⇒ 3 6/7

Now, We can change the fraction into an improper fraction as,

⇒ 3 6/7

⇒ (3×7 + 6)/7

⇒ (21 + 6)/7

⇒ 27/7

Therefore, an improper fraction in the lowest term is,

⇒ 27/7

To learn more about the fraction visit:

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#SPJ6

Answer:

a) - 10m

b) - $5000

c) - 40°

d) + $2000

Step-by-step explanation:

I hope this help you

Answer:

95.06506849315

Step-by-step explanation:

Basically 95 years old which is very old Pls brainliest Thx! :D

Answer:

lets see according to my cackulations.... suzie would be, 6.....she would be six feet under the ground. dead. deceaced.gone.

Step-by-step explanation:

Answer:

what following data

Step-by-step explanation:

            4^t × 2^t = 2^what         [convert all terms to the same base (2)]

∴   2^t × 2^t × 2^t = 2^what       [use the multiplicat law of exponents]

              2^(t+t+t) = 2^what       [simplify]

                   2^3t =  2^what