यदि $\dfrac {cos x + sin x}{cos x} = \sqrt {2}$ है, तो $\dfrac {cos x – sin x }{sin x }$ के मानों में से एक है?
Solution
$\dfrac{\cos x + \sin x}{\cos x} = \sqrt{2}$
$\cos x + \sin x = \sqrt{2} \cos x$
$\sin x = \sqrt{2} \cos x - \cos x$
$\sin x = \cos x (\sqrt{2} - 1)$
$\sin x (\sqrt{2} + 1) = \cos x (\sqrt{2} - 1)(\sqrt{2} + 1)$
$\sin x (\sqrt{2} + 1) = \cos x$
$\sqrt{2} \sin x + \sin x = \cos x$
$\sqrt{2} = \dfrac{\cos x - \sin x}{\sin x}$