Question

cot theta minus tan theta equals 2cos square theta minus 1 whole divided by sin theta cos theta

Answer 1

it is very ezy just needs conversion of tan and cot theta

Answer 2

Answer:

We have to prove,

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

L.H.S.

$=cot \theta - tan \theta$

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

( Because, cot A = cos A / sin A and tan A = sin A / cos A )

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

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

( Because, cos 2A = cos² A - sin² A )

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

( Because, cos 2 A = 2 cos² A - 1 ),

= R.H.S.

Hence, proved.