Question

Help me for this question​

Answer 1

Note that $sin^{2}x +cos^{2}x =1$

Then,

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

Hence, shown