Question

Solve Cosx/(1-sinx) + cosx/(1+sinx) =4​

Answer 1

$\\ \\</p><p> \frac{ \cos x }{ 1 - \sin x} + \frac{ \cos x }{1 + \sin x} = 2 \; \sec x \\ \\ Solving \: L.H.S, \\ \\ \Rightarrow \qquad \frac{ \cos x }{ 1 - \sin x } + \frac{ \cos x }{1 + \sin x} \\ \\ \Rightarrow \qquad \frac{ \cos x(1 + \sin x) + \cos x (1 - \sin x ) }{ (1 - \sin x)(1 + \sin x) } \\ \\ \Rightarrow \qquad \frac{ \cos x ( 1 \cancel{+ \sin x} + 1 \cancel{- \sin x}) }{ 1^2 - \sin^{2} x } \qquad \qquad \left( \because \; (a-b)(a+b) = a^2 - b^2 \right) \\ \\ \Rightarrow \qquad \frac{ 2\; \cancel{\cos x} }{ \cos^{\cancel{2}} x } \qquad \qquad \left( \because \; \sin^{2} \theta + \cos^{2} \theta = 1 \right) \\ \\ \Rightarrow \qquad 2 \times \frac{1}{ \cos x } \\ \\ \Rightarrow \qquad \bold{2 \; \sec x} \qquad \qquad \left( \because \cos x = \frac{1}{\sec x} \right) </p><p>$