Question

Prove that 1/sin^2A -1/tan^2A= 1

Answer 1

Explanation:

`LHS =(1)/(Sin^(2) \ A )-(1)/(Tan^(2) \ A )\\\\\\ = (1)/(sin^(2) \ A)- (1)/((Sin^(2) \ A)/(Cos^(2) \ A))\\\\\\= (1)/(sin^(2) \ A ) - (Cos^(2) \ A)/(Sin^(2) \ A)\\\\\\= (1-Cos^(2) \ A)/(Sin^(2) \ A)\\\\\\= (Sin^(2) \ A)/(Sin^(2) \ A)\\\\\\= 1 = \ RHS`

Hint: 1 - Cos² A = Sin² A