Question

1 - cosα/sinα = sinα/1+cosα​

Answer 1

Question:-

$\rm \:prove \: that : \frac{1 - \cos\alpha }{ \sin \alpha } = \frac{ \sin \alpha }{1 + \cos \alpha }$

Solution:-

$\frac{1 - \cos\alpha }{ \sin \alpha } = \frac{ \sin \alpha }{1 + \cos \alpha }$

Using cross multiplication ; we get

$\rm \: (1 - \cos\alpha)(1 + \cos \alpha ) = \sin {}^{2} \alpha$

Use this identity

$\rm \: (a + b)(a - b) = ( {a}^{2} - {b}^{2} )$

We get

$\rm \: (1 - \cos {}^{2} \alpha ) = \sin {}^{2} \alpha$

$1 = \sin {}^{2} \alpha + \cos {}^{2} \alpha$

By using trigonometry identity

$\sin {}^{2} \alpha + \cos {}^{2} \alpha = 1$

we get

$\rm \: 1 = 1$

Hence proved