Question

Find the general solution of sin 2 theta = cos3 theta

Answer 1

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Answer 2

Answer:

The General Solution is $2k\pi+\frac{\pi}{10}$

Step-by-step explanation:

We have to find general solution of $sin\,2\theta=cos\,3\theta$

Consider the statement,

$sin\,2\theta=cos\,3\theta$

$sin\,2\theta=sin(90-\,3\theta)$  ( cos x = sin ( 90 - x ) )

$\implies 2\theta=90-\,3\theta$

$5\theta=90$

$\theta=\frac{90}{5}$

$\theta=18^{\circ}$

$\theta=\frac{\pi}{10}$

So the General solution is $\theta=2k\pi+\frac{\pi}{10}$  where, k is any integer

Therefore, The General Solution is $2k\pi+\frac{\pi}{10}$