# Solving a trigonometric equation

• Apr 26th 2009, 09:35 AM
blue_blue
Solving a trigonometric equation
sin a + sin 3a = cos a + cos 3a
• Apr 27th 2009, 08:32 AM
red_dog
Use $\sin a+\sin b=2\sin\frac{a+b}{2}\cos\frac{a-b}{2}$ and $\cos a+\cos b=2\cos\frac{a+b}{2}\cos\frac{a-b}{2}$

Then,

$2\sin 2a\cos a=2\cos 2a\cos a$

$2\cos a(\sin 2a-\cos 2a)=0$

Now you have to solve the equations:

$\cos a=0$ and $\sin 2a-\cos 2a=0\Leftrightarrow \tan 2a=1$

Can you do that?