Question

Period of $\frac{sin\theta +sin2\theta }{cos\theta +cos2\theta }$ is

• A. $2\pi$
• B. $\pi$
• C. $\frac{2\pi }{3}$
• D. $\frac{\pi }{3}$

Answer 1

Answer: (C)

$\frac{sin\theta +sin2\theta }{cos\theta +cos2\theta }=\frac{2sin\left(\frac{3\theta }{2}\right)cos\left(\frac{\theta }{2}\right)}{2cos\left(\frac{3\theta }{2}\right)cos\left(\frac{\theta }{2}\right)}=tan\left(\frac{3\theta }{2}\right)$
Hence period $=\frac{2\pi }{3}$