Question

2.) Fill in the blank.

Answer 1

Answer:

E.) 1

Step-by-step explanation:

Firstly we will solve for L.H.S.

L.H.S. =$Csc^2\theta$

Since we know that $Csc^2\theta$ is the inverse of $Sin^2\theta$.

So we can say that;

$csc^2\theta=\frac{1}{sin^2\theta}$

Now For R.H.S.

$Cot^2\theta+1$

Since we  can rewrite $cot^2\theta$ as $\frac{cos^2\theta}{sin^2\theta}$.

Now we can say that the R.H.S. is;

$\frac{cos^2\theta}{sin^2\theta}+1$

Now we add the fraction and get;

$\frac{cos^2\theta+sin^2\theta}{sin^2\theta}$

Now according to trigonometric identity;

$cos^2\theta+sin^2\theta=1$

So, $\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}$

Here,

$csc^2\theta=\frac{1}{sin^2\theta}$   and     $Cot^2\theta+1$ = $\frac{1}{sin^2\theta}$  

L.H.S. = R.H.S.

Hence $csc^2\theta=cot^2\theta+1$