Question

Trigonometries easy sum​

Answer 1

Step-by-step explanation:

$\sqrt{ \frac{1 - \sin( \alpha ) }{1 + \sin( \alpha ) } } \\ \sqrt{ \frac{ {( \sin( \frac{ \alpha }{2} ) - \cos( \frac{ \alpha }{2} )) }^{2} }{ {( \sin( \frac{ \alpha }{2} ) + \cos( \frac{ \alpha }{2} )) }^{2} } } \\ \frac{ \sin( \frac{ \alpha }{2} ) - \cos( \frac{ \alpha }{2} ) }{ \sin( \frac{ \alpha }{2} ) + \cos( \frac{ \alpha }{2} ) } \\ on \: rationalising \: \\ \frac{ {( \sin( \frac{ \alpha }{2} ) - \cos( \frac{ \alpha }{2} )) }^{2} }{ \cos( \alpha ) } \\ \frac{1 - \sin( \alpha ) }{ \cos( \alpha ) } \\ \sec( \alpha ) - \tan( \alpha ) \\ hence \\ lhs = rhs \\ proved$