Question

Verify the identity

`csc^(2)x-csc^(2)xcos^(2)x=1`

Answer 1

The answer to your question is below

Explanation:

csc²x - csc²x cos²x = 1

Process

1.- Convert the second term to sines

csc²x - cos²x/sin²x = 1

2.- Convert cos²x/sin²x to cot²x

csc²x - cot²x = 1

3.- Solve for csc²x

csc²x = 1 + cot²x

We have verified it, because there is a Pythagorean identity which sets that

csc²x = 1 + cot²x