Question

Simplify the following expression:
$\frac{1+\sin +2x}{(\sin x+\cos x{)}^2}$

Answer 1

$=\frac{1+\sin 2x}{{(\sin x+\cos x)}^2}=\frac{si{n}^{2}x+{\cos }^{2}x+\sin 2x}{{(\sin x+\cos x)}^2}$

$[\because 1={\sin }^{2}x+co{s}^{2}x]$

$=\frac{{\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x}{{(\sin x+\cos x)}^2}=\frac{{(\sin x+\cos x)}^2}{{(\sin x+\cos x)}^2}[\because (a+b{)}^2=a^2+b^2+2ab]$

$=1$