Question

PT- Tan^2Q +cot^2Q + 2 = sec^2 - cosec^2Q

Answer 1

2sec2θ-sec4θ-2cosec2θ+cosec4θ = 2sec2θ – 2cosec2θ – sec4θ + cosec4θ
= 2(sec2θ – cosec2θ) – (sec4θ –  cosec4θ)
= 2(sec2θ – cosec2θ) – (sec2θ – cosec2θ) (sec2θ + cosec2θ)
= (sec2θ – cosec2θ)[2 – (sec2θ + cosec2θ)]
= (sec2θ – cosec2θ)[2 – (1 + tan2θ + 1 + cot2θ)]
= (1 + tan2θ – 1 – cot2θ)[2 – (2 + tan2θ + cot2θ)]
= (tan2θ – cot2θ) [2 – 2 – tan2θ – cot2θ)]
= (tan2θ – cot2θ) × – [tan2θ + cot2θ)]
= (cot2θ – tan2θ) × [cot2θ + tan2θ)]
= cot4θ – tan4θ
=