Answer: The identity is verified. See the explanation.
Step-by-step explanation:
You must keep on mind the following identities:
[tex]csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1[/tex]
Therefore, by substitution, you can rewrite the identity as shown below:
[tex]1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta[/tex]
Simpliying, you obtain:
[tex]\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta[/tex]
The identity is verified.
