Question

prove identity.

4cot theta/1+cot^2 theta = 2sin2theta

Answer 1

\[\frac{4 \cot (\theta)}{cosec^2 (\theta)} \implies 4 \frac{\cos(\theta)}{\sin (\theta)} \times \sin^2 (\theta) = 2 \times 2\sin(\theta)\cos(\theta) = 2\sin(2\theta)\]

Answer 2

Using:

\[\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}\]

\[\frac{1}{cosec^2(\theta)} = \sin^2 (\theta)\]

Answer 3

\[(4\cos \theta/\sin \theta)/cosec^2 \theta\] =\[4\cos \theta \sin \theta \sin \theta / \sin \theta\] =\[2 \times 2\sin \theta \cos \theta = \sin 2 \theta\]

Answer 4

damn u r fast

Answer 5

thank you all ;]