Question

(tanA+1/cosA)^2+(tanA-1/cosA)^2=2(1+sin^2A/1-sin^2A)

Answer 1

LHS
${( \tan \alpha + \frac{1}{ \cos \alpha } )}^{2} +( \tan \alpha - \frac{1}{ \cos \alpha }) { }^{2} \\ = ( \frac{ \sin\alpha }{ \cos \alpha } + \frac{1}{ \cos\alpha } ) {}^{2} + ( \frac{ \sin \alpha }{ \cos\alpha } - \frac{1}{ \cos\alpha }) {}^{2} \\ = \frac{2( \sin {}^{2} \alpha + 1) }{ \cos {}^{2} \alpha }$
RHS
2 (1+ sin²α)/(1- sin²α)
2 ( sin²α+1)/cos²α
LHS = RHS