Question

Period of $\cos \frac{3x}{5}+2\sin \frac{2x}{7}-5\cot 4x$ is

• A. $7\pi$
• B. $14\pi$
• C. $28\pi$
• D. $70\pi$

Answer 1

The correct option is D $70\pi$

Period of $cos\frac{3x}{5}=\frac{2\pi }{3}\times 5=\frac{10\pi }{3}$
Period of $sin\frac{2x}{7}=\frac{14\pi }{2}=7\pi$
Period of $cot14x=\frac{\pi }{14}$
$\therefore$ Period of $f\left(x\right)=cos\frac{3x}{5}+2sin\frac{2x}{7}-5cot14xisLCM(\frac{10\pi }{3},7\pi ,\frac{\pi }{14})$
$\therefore LCM=\frac{70\pi }{1}=70\pi$
$[LCMof(\frac{p}{r},\frac{q}{s})=\frac{LCMof(p,q)}{HCFof(r,s)}]$