Question

If sin θ +cosec θ = 2 then sin2θ+ cosec2θ is equal to

a) 1 b) 4

c) 2 c) 9

Answer 1

Answer:

C

Step-by-step explanation:

We are given that:

$\sin \theta +\csc \theta = 2$

And we want to find the value of:

$\sin^2\theta + \csc^2\theta$

From the first equation, we can square both sides:

$(\sin \theta + \csc \theta)^2=(2)^2$

Square:

$\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4$

Let csc(θ) = 1 / sin(θ):

$\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4$

Simplify:

$\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4$

Therefore:

$\sin ^2\theta + \csc^2\theta =2$

Our answer is C.

Answer 2

B) 4 is the answer I believe