Question

Prove that √(1-cos a)/(1+cos a) = cosec a - cot a​

Answer 1

Step-by-step explanation:

let theta be alpha oke

takin LHS

now,

$\sqrt{ \frac{1 - cos \alpha }{1 + \cos\alpha } } \\ \sqrt{ \frac{1 - \cos\alpha }{1 + \cos \alpha } \times \frac{1 - \cos \alpha }{1 - \cos\alpha } } \\ \sqrt{ \frac{(1 - \cos\alpha) {}^{2} }{1 - ( \cos \alpha {}^{2} ) } } \\ \sqrt{ \frac{(1 - \cos \alpha) {}^{2} }{ \sin {}^{2} \alpha } } \\ \frac{1 - \cos \alpha }{ \ \sin \alpha } \\ \frac{1}{ \sin\alpha } - \frac{ \cos \alpha }{ \sin \alpha } \\ \csc \alpha - \cot \alpha = rhs \\ proved$