Question

Pls someone help , can't find the solution anywhere ​

Answer 1

Answer:

Explanation:
GIVEN : SinθCosθ / (Cosθ - Sinθ) (Cosθ + Sinθ) = tanθ / 1- tan²θ

To prove : L.H.S.= R.H.S

Proof : Take Left hand side ( L.H.S) Part ,

SinθCosθ / (Cosθ - Sinθ) (Cosθ + Sinθ)

We can clearly see that , we can solve the denominator,

SinθCosθ/ Cos²θ - Sin²θ -(1) [ (a+b)(a-b)
= a²-b² ]

Now , Divide above Equation by Cos²θ ;
So we have ,
(SinθCosθ/Cos²θ)/[(Cos²θ/Cos²θ)- (Sin²θ/Cos²θ)]

= (Sinθ/ Cosθ) / [1- (Sin²θ/Cos²θ)]

= tanθ / 1- tan²θ

= R.H.S

So, L.H.S = R.H.S