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  4. Period of (sin θ +sin 2θ /cos θ + cos 2θ ) is

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Q. Period of $\frac{sin\,\theta +sin\,2\theta }{cos\,\theta + cos\,2\theta } $ is

Trigonometric Functions

Solution:

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