Question

2cos^2 theta-1÷cot theta-tan theta=sin theta.cos theta

Answer 1

To Prove :-

$\pink{\bf\dfrac{2Cos²θ - 1 }{Cotθ - tanθ} = Sinθ.Cosθ}$

Proof :-

Taking L.H.S

$\green{\bf\dfrac{Cos²θ +Cos²θ - 1 }{\dfrac{Cosθ}{Sinθ} - \dfrac{Sinθ}{Cosθ}}}$

$\green{\bf\dfrac{Cos²θ - Sin²θ }{Cos²θ - Sin²θ} × Sinθ.Cosθ}$

$\sf\blue{=> Sinθ.Cosθ}$

$\sf{\fbox{L.H.S = R.H.S}}$