Question

1-sin^2 theta/1+cos theta

Answer 1

$\implies\sf \dfrac{1-sin^2\theta}{1+cos\theta}\\ \\ \\ :\implies\sf \dfrac{1-\big\lgroup 1-cos^2\theta\big\rgroup}{1+cos\theta}\\ \\ \\ \star\ \underline{\sf\ sin^2\theta= (1-cos^2\theta)}\\ \\ \\ :\implies\sf \dfrac{1-(1-cos\theta)\cancel{(1+cos\theta)}}{\cancel{1+cos\theta)}}\\ \\ \\ :\star\underline{\sf\ a^2-b^2=(a-b)(a+b)}\\ \\ \\ :\implies\sf 1-(1-cos\theta)\\ \\ \\ :\implies 1-1+cos\theta\\ \\ \\ {\boxed{\sf\ \ cos\theta}}$