Question

Prove that ${\left(1-\sin \theta +\cos \theta \right)}^2=2(1+\cos \theta )(1-\sin \theta )$

Answer 1

$(1-sin\theta +cos\theta {)}^2$

$\Rightarrow (1-sin\theta {)}^2+co{s}^2\theta +2(1-sin\theta \left)\right(cos\theta )$

$\Rightarrow 1+si{n}^2\theta -2sin\theta +co{s}^2\theta +2(1-sin\theta )\left(cos\theta \right)$

$\Rightarrow 2-2sin\theta +2(1-sin\theta )\left(cos\theta \right)$

$\Rightarrow 2(1-sin\theta )+2(1-sin\theta )\left(cos\theta \right)$

$\Rightarrow 2(1-sin\theta )(1+cos\theta )$

Hence proved.