The period of frac{sin x}{cos 3x} + frac{sin | vedclass

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

Question

(D) Let $f(x) = \frac{\sin x}{\cos 3x} + \frac{\sin 3x}{\cos 9x} + \frac{\sin 9x}{\cos 27x} + \frac{\sin 27x}{\cos 81x}$.Using the identity $	an 	he

Vedclass · Accepted Answer

$\pi$

Vedclass · Answer

(D) Let $f(x) = \frac{\sin x}{\cos 3x} + \frac{\sin 3x}{\cos 9x} + \frac{\sin 9x}{\cos 27x} + \frac{\sin 27x}{\cos 81x}$.Using the identity $	an 	heta - 	an \phi = \frac{\sin(	heta - \phi)}{\cos 	heta \cos \phi}$,we can rewrite each term:$\frac{\sin x}{\cos 3x} = \frac{1}{2} \frac{\sin(3x - x)}{\cos 3x \cos x} = \frac{1}{2}(	an 3x - 	an x)$.Similarly,$\frac{\sin 3x}{\cos 9x} = \frac{1}{2}(	an 9x - 	an 3x)$,$\frac{\sin 9x}{\cos 27x} = \frac{1}{2}(	an 27x - 	an 9x)$,$\frac{\sin 27x}{\cos 81x} = \frac{1}{2}(	an 81x - 	an 27x)$.Summing these,we get $f(x) = \frac{1}{2}(	an 81x - 	an x)$.The period of $	an(kx)$ is $\frac{\pi}{|k|}$.The period of $	an 81x$ is $\frac{\pi}{81}$ and the period of $	an x$ is $\pi$.The period of the sum is the $L$.$C$.$M$. of the individual periods: $	ext{L.C.M.}\left(\frac{\pi}{81}, \piight) = \pi$.

The period of $\frac{\sin x}{\cos 3x} + \frac{\sin 3x}{\cos 9x} + \frac{\sin 9x}{\cos 27x} + \frac{\sin 27x}{\cos 81x}$ is

Similar Questions

The period of $\sin^2 x$ is

The period of the function $\sin \left( \frac{\pi x}{2} \right) + \cos \left( \frac{\pi x}{2} \right)$ is

The period of $\sin \frac{x}{2} - \cos \frac{x}{3}$ is (in $\pi$)

If $f(x) = \sin^2\left(\frac{\pi}{8} + \frac{x}{2}\right) - \sin^2\left(\frac{\pi}{8} - \frac{x}{2}\right)$,then the period of $f$ is

The period of the function $f(x) = \log(\cos 2x) + \sin 4x$ is :-

Vedclass Test Series

Exam Paper Generator

Online Exam Module