Question

prove that (1 - cos²A) cosec²A =
1​

Answer 1

The following is a trigonometric identity:

sec2A−sin2Atan2A=csc2A−cos2A

Rewrite the left-hand side entirely in terms of sin and cos , obtaining:

sec2A−sin2Atan2A=1cos2A−sin2Asin2Acos2A

Now, multiply the top and bottom by cos2A:

1cos2A−sin2Asin2Acos2A=1−sin2Acos2Asin2A

Then, split up the fraction into two terms:

1−sin2Acos2Asin2A=1sin2A−sin2Acos2Asin2A=1sin2A−cos2A

Finally, use the definition of csc to obtain the identity:

sec2A−sin2Atan2A=csc2A−cos2A

I hope you are understand my solution