1.

Prove the following:(tan θ + 1/cos θ)2 + (tan θ - 1/ cos θ)2 = 2 (1+sin2θ/1-sin2θ)

Answer»

L.H.S. = (tan θ + 1/cos θ)2 + (tan θ - 1/cos θ)2 

= (tanθ + secθ)2 + (tanθ – secθ)2 

= tan2 θ + 2 tan θ sec θ + sec2 θ + tan2 θ – 2 tan θ sec θ +.sec2 θ 

= 2(tan2 θ + sec2 θ)



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