Question

Prove this identity:

csc^2θ + sec^2θ = csc^2θ*sec^2θ

Answer 1

Hi ,

Here I used A instead of theta

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We know that ,

1 ) Cosec A = 1/ sinA

2 ) secA = 1/ cosA

3 ) sin² A + cos² A = 1

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LHS = cosec²A + sec²A

= 1/ sin² A + 1/ cos² A

= ( Cos² A + sin² A ) / sin²Acos² A

= 1 / sin² Acos² A

= Cosec² A sec² A

= RHS

I hope this helps you.
:)