Question

Cot theta _tan theta=cos² theta_1/sin theta.cos theta prove .​

Answer 1

Step-by-step explanation:

The expression given in the question can be proved by making LHS = RHS

In LHS we have,

$cot \theta - tan \theta$

and in the RHS we have prove it to $=\frac{2 cos^2 \theta - 1}{sin \theta cos\theta}$ .

Method,

L.H.S. = $cot \theta - tan \theta$

We know,

( cot X = cos X / sin X and tan X = sin X / cos X )

∴ LHS $=\frac{ cos^2 \theta - sin^2 \theta }{sin \theta cos \theta}$

$=\frac{cos 2\theta}{sin \theta cos \theta}$

We also know, ( cos 2 X = cos² X - sin² X ) & ( cos 2X = 2cos² X - 1 )

$=\frac{2 cos^2 \theta - 1}{sin \theta cos\theta}$  

= RHS

Hence proved.