Question

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

Answer 1

True

Explanation:

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

To find: False or True

Taking left side of equation

`\Rightarrow \csc^2x-1`

`\Rightarrow (1)/(\sin^2)-1`
`\because \csc x=(1)/(\sin x)`

`\Rightarrow (1-\sin^2x)/(\sin^2)`

`\Rightarrow (\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.