Question

Solve:

Answer 1

Answer:

I hope it'll help you...

Answer 2

To prove :

$\sqrt{ \frac{1 + cosθ}{1 - cosθ}} = cosecθ+cotθ$

Solution:

$L.H.S. = \sqrt{ \frac{1+cosθ}{1−cosθ}}$

Multiplying numerator and denominator with 1+cos θ we get,

$= \sqrt{ \frac{1+cosθ}{1−cosθ } \times\frac{1+cosθ}{1+cosθ} }$

$= \sqrt{ \frac{(1 + cosθ {)}^{2} }{1 - cos^{2} θ} }$

$= \sqrt{ \frac{(1+cosθ)^{2}}{sin^{2}θ} }$

$= \frac{1+cosθ}{ \sinθ}$

$= \frac{1}{sinθ} + \frac{ \cosθ}{sinθ}$

$=cosec \: θ+cot \: θ$

$= R.H.S.$