Question

Prove that (1+sin theta -cos theta/1+sin theeta+cos theeta)^2 =1-cos theeta /1+cos theeta

Answer 1

Answer:

Step-by-step explanation:

(1+sinθ - cosθ/1+sinθ + cosθ)²

= (1+sinθ)² + Cos²θ - 2(1+Sinθ)(Cosθ)/ (1+sinθ)² + Cos²θ + 2(1+Sinθ)(Cosθ)

= 1 + Sin²θ + 2Sinθ+Cos²θ - 2(Cosθ + CosθSinθ)/ 1 + Sin²θ + 2Sinθ+Cos²θ + 2(Cosθ + CosθSinθ)

= 2 + 2(Sinθ - Cosθ - CosθSinθ)/2 + 2(Sinθ + Cosθ+ CosθSinθ)

= 1 + Sinθ - Cosθ - CosθSinθ / 1 + Sinθ + Cosθ + CosθSinθ

= (1 + Sinθ) - Cosθ(1+Sinθ)/ (1 + Sinθ)+ Cosθ(1 + SInθ)

= (1 + Sinθ) ( 1 - Cosθ) / (1 + Sinθ)( 1+Cosθ)

= 1 - Cosθ / 1 + Cosθ

= R.H.S

Hence proved.