If A is not an integral multiple of frac{pi}{ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We have $\operatorname{cosec} 2A + \cot 2A = \frac{1}{\sin 2A} + \frac{\cos 2A}{\sin 2A} = \frac{1 + \cos 2A}{\sin 2A}$.Using the identities $1 +

Vedclass · Accepted Answer

$	an A + 2 \cot 2A$

Vedclass · Answer

(C) We have $\operatorname{cosec} 2A + \cot 2A = \frac{1}{\sin 2A} + \frac{\cos 2A}{\sin 2A} = \frac{1 + \cos 2A}{\sin 2A}$.Using the identities $1 + \cos 2A = 2 \cos^2 A$ and $\sin 2A = 2 \sin A \cos A$,we get:$\frac{2 \cos^2 A}{2 \sin A \cos A} = \frac{\cos A}{\sin A} = \cot A$.Now,we express $\cot A$ in terms of $	an A$:$\cot A = \frac{1}{	an A} = \frac{	an^2 A + 1 - 	an^2 A}{	an A} = 	an A + \frac{1 - 	an^2 A}{	an A}$.Since $	an 2A = \frac{2 	an A}{1 - 	an^2 A}$,we have $\cot 2A = \frac{1 - 	an^2 A}{2 	an A}$,which implies $\frac{1 - 	an^2 A}{	an A} = 2 \cot 2A$.Therefore,$\operatorname{cosec} 2A + \cot 2A = 	an A + 2 \cot 2A$.

If $A$ is not an integral multiple of $\frac{\pi}{2}$,then $\operatorname{cosec} 2A + \cot 2A$ is equal to

Similar Questions

$(1+\sec 2\theta)(1+\sec 4\theta) = $

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?

Prove that $\frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} = 2 \sin x$.

$\tan \alpha + 2 \tan 2 \alpha + 4 \tan 4 \alpha + 8 \cot 8 \alpha = $

If $\cos A = \frac{7}{25}$ and $\frac{3 \pi}{2} < A < 2 \pi$,then $\cos \frac{A}{4} + \cos \frac{A}{2} - \cos 2A =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module