# Math Help - [SOLVED] Proving

1. ## [SOLVED] Proving

Without using a calculator, prove that $x = \frac{\pi}{10}$ satisfies the equation $\sin 3x = \cos 2x$.

2. Originally Posted by mark1950
Without using a calculator, prove that $x = \frac{\pi}{10}$ satisfies the equation $\sin 3x = \cos 2x$.
$\cos(2x) = \sin\left(\frac{\pi}{2} - 2x\right)$

for $x = \frac{\pi}{10}$ ...

$\sin\left(\frac{\pi}{2} - \frac{2\pi}{10}\right) = \sin\left(\frac{3\pi}{10}\right) = \sin(3x)$