Question

Cot²a-cos²a=cot²a.cos²a

Answer 1

SolUtion :

$\sf Cot^2\: A - Cos^2\:A = Cot^2\: A . Cos^2\:A$

L.H.S =

$\sf\dfrac{Cos^2\:A}{Sin^2\:A} - Cos^2$

$\sf\dfrac{Cos^2\:A-Cos^2\:A\times Sin^2\:A}{Sin^2\:A}$

$\sf\dfrac{Cos^2\:A(1-Sin^2\:A)}{Sin^2\:A}$

$\sf\dfrac{Cos^4\:A}{Sin^2\:A}$

Now,

R.H.S :

$\sf Cos^2\:A \times \dfrac{Cos^2\:A}{Sin^2\:A}$

$\sf =\dfrac{Cos^4\:A}{Sin^2\:A}$

Here,

L.H.S = R.H.S

Hence proved!

$\rule{200}2$