Question

Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ

Answer 1

Answer: The identity is verified. See the explanation.

Explanation:

You must keep on mind the following identities:

`csc\theta=(cos\theta)/(sin\theta)\\\\csc\theta=(1)/(sin\theta)\\\\sin^2\theta+cos^2\theta=1`

Therefore, by substitution, you can rewrite the identity as shown below:

`1+cot^2\theta=csc^2\theta\\\\1+(cos^2\theta)/(sin^2\theta)=csc^2\theta`

Simpliying, you obtain:

`(sin^2\theta+cos^2\theta)/(sin^2\theta)=csc^2\theta\\\\(1)/(sin^2\theta)=csc^2\theta\\\\csc^2\theta=csc^2\theta`

The identity is verified.