# Math Help - Trig equations

1. ## Trig equations

Find the general solution of equation sin2x=cosx

2. $\sin 2x=\sin\left(\frac{\pi}{2}-x\right)$

$\sin 2x-\sin\left(\frac{\pi}{2}-x\right)=0$

Now use the identity $\sin a-\sin b=2\sin\frac{a-b}{2}\cos\frac{a+b}{2}$

3. Originally Posted by requal
Find the general solution of equation sin2x=cosx
$\sin(2x) = \cos{x}$

$2\sin{x}\cos{x} = \cos{x}$

$2\sin{x}\cos{x} - \cos{x} = 0$

$\cos{x}(2\sin{x} - 1) = 0$

set each factor equal to zero and solve.

4. Originally Posted by requal
Find the general solution of equation sin2x=cosx

$\sin 2x=\cos x$

$2\sin x\cos x = \cos x$

$2\sin x \cos x - \cos x =0$

$\cos x(2\sin x -1 )=0$

$\cos x = 0 \Rightarrow x=\frac{\pi}{2} + n\pi$

$\sin x =\frac{1}{2} \Rightarrow x=\frac{\pi}{6} + 2n\pi$ and $x=\frac{5\pi}{6}+2n\pi$