Answer:
[tex]\text{Solution:}[/tex]
[tex]\text{L.H.S. = }\dfrac{1}{1-\sin x}+\dfrac{1}{1+\sin x}[/tex]
[tex]=\dfrac{1+\sin x}{(1-\sin x)(1+\sin x)}+\dfrac{1-\sin x}{(1+\sin x)(1-\sin x)}[/tex]
[tex]=\dfrac{1+\sin x}{1-\sin^2 x}+\dfrac{1-\sin x}{1-\sin ^2x}[/tex]
[tex]=\dfrac{1+\sin x}{\cos^2 x}+\dfrac{1-\sin x}{\cos^2 x}[/tex]
[tex]=\dfrac{1+\sin x+1-\sin x}{\cos ^2x}[/tex]
[tex]=\dfrac{2}{\cos^2 x}[/tex]
[tex]=2\sec^2 x[/tex]
