Question

(1-cosx/1+cosx)^1/2=cosec x -cot x

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\sqrt{\dfrac{1-cos(x)}{1+cos(x)}}}$

$\sf{=\sqrt{\dfrac{(1-cos(x))(1-cos(x))}{(1+cos(x))(1-cos(x))}}}$

$\sf{=\sqrt{\dfrac{(1-cos(x))^2}{1-cos^2(x)}}}$

$\sf{=\sqrt{\dfrac{(1-cos(x))^2}{sin^2(x)}}}$

$\sf{=\dfrac{1-cos(x)}{sin(x)}}$

$\sf{=\dfrac{1}{sin(x)}-\dfrac{cos(x)}{sin(x)}}$

$\sf{=cosec(x)-cot(x)}$