Question

True or false. The equation csc^2x-1=cot^2x is an identity.

Answer 1

Answer:

True

Step-by-step explanation:

Given: $\csc^2x-1=\cot^2x$

To find: False or True

Taking left side of equation

$\Rightarrow \csc^2x-1$

$\Rightarrow \dfrac{1}{\sin^2}-1$                          $\because \csc x=\dfrac{1}{\sin x}$

$\Rightarrow \dfrac{1-\sin^2x}{\sin^2}$

$\Rightarrow \dfrac{\cos^2x}{\sin^2}$                          $\because 1-\sin^2x=\cos^2$

$\Rightarrow \cot^2x$

Thus, The left hand side is equal to right ahnd side.

Hence, The statement is true.

Answer 2

Csc² x - 1 = cot² x
1/ sin² x - 1 = cot² x
( 1 - sin² x ) / sin² x = cot² x
cos² x / sin² x = cot² x
cot² x = cot² x
Answer: True.