Analytical Trigonometry: proving identities: prove that the expression: 1 + cos²ß = csc²ß - cot²ß + sin²ß.

Question

*transposition is not allowed in proving identities in trigonometry

*my math HW :P

Answer 1

This is not an identity.

Let's start with the right hand side.

Right hand side = csc²ß - cot²ß + sin²ß
= (csc²ß - cot²ß) + sin²ß = 1 + sin²ß ≠ 1 + cos²ß

Right hand side ≠ Left hand side

Answer 2

csc²ß - cot²ß = 1, so this is only true when: cos²ß = sin²ß. More specifically, when ß = pi/4 + npi/2 for any integer n.

Answer 3

I think that there is an error in your question.
However I will proceed on the basis of what is given:-

RHS = 1/sin² ß - cos² ß /sin² ß + sin² ß

RHS = [1 - cos² ß + sin^(4) ß ] / sin² ß

RHS = [ sin² ß + sin^(4) ß ] / sin² ß

RHS = sin² ß [ 1 + sin² ß] / sin² ß

RHS = 1 + sin² ß

Over to you!