Question

Find the fundamental period for $f\left(x\right)=\cos \frac{3}{5}x-\sin \frac{3}{7}x$

• A. $70\pi$
• B. $28\pi$
• C. $140\pi$
• D. $5\pi$

Answer 1

The correct option is A $70\pi$

$f\left(x\right)=\cos \frac{3}{5}x-\sin \frac{3}{7}x$
Period of $\cos \frac{3}{5}x$ is $\frac{2\pi \times 5}{3}=\frac{10\pi }{3}$
Period of $\sin \frac{3}{7}x$ is $\frac{2\pi \times 7}{3}=\frac{14\pi }{3}$
Therefore their L.C.M is $70\pi$