Question

Prove:-
$1+\frac{{\cot }^2\alpha }{1+\cos ec\alpha }=\cos ec\alpha$

Answer 1

Now,

$1+\frac{{\cot }^2\alpha }{1+\cos ec\alpha }$

$=$$1+\frac{{\cot }^2\alpha (\cos ec\alpha -1)}{-1+\cos e{c}^2\alpha }$

$=$$1+\frac{{\cot }^2\alpha (\cos ec\alpha -1)}{{\cot }^2\alpha }$ [ Since $\cos e{c}^2\alpha -{\cot }^2\alpha =1$]

$=1+\cos ec\alpha -1$

$=\cos ec\alpha$.