Question

verify the identity
$csc^{2}x-csc^{2}xcos^{2}x=1$

Answer 1

Answer:

The answer to your question is below

Step-by-step 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