Question

Prove that (cotA-cosA)/(cotA+cosA) = (cosecA-1)/(cosecA+1)

Answer 1

lhs = (cotA - cosA)/(cotA+cosA)
=(cosA/sinA - cosA)/(cosA/sinA + cosA)

=cosA(1/sinA - 1)/cosA(1/sinA + 1)

= (1/sinA -1)/(1/sinA+1)
=(cosecA-1)/(cosecA+1) since 1/sinA= cosecA
=rhs

Answer 2

Hi there ♥️

$\frac{ \cot\alpha - cosa }{cota \: + \: cosa} = \\ \\ \frac{ \frac{cosa}{sina} - cosa}{ \frac{cosa}{sina} + cosa }$
$\frac{cosa( \frac{1}{sina \: } - 1) }{cosa (\frac{1}{sina} + 1)} \\ \\ = \frac{ \frac{1}{sina} - 1}{ \frac{1}{sina} + 1} = \\ \\ \frac{coseca - 1}{coseca + 1}$

=RHS

Hence proved ✅✅

Thanks :)