Question

Solve the equation: for 0° ≤ x ≤ 360°

cos (45° + x) + cos (45° - x) = √ 6 sin x

Answer 1

use angle sum/difference identities

Answer 2

We know that :
\[\cos (a+b)+\cos(a-b)=2\cos a\cos b\]
So use this formula to find that :
\[2\cos 45^\circ\cos x=\sqrt6\sin x\]
Can you continue from here ?

Answer 3

Thanks! let me disgust =)

Answer 4

May I know how to get √6 sinx = 2 cos a cos b?

Answer 5

Look !
The left side of the equation is :
\[\cos (45° + x) + \cos (45° - x)\]
which equals :
\[2\cos 45^\circ\cos x\]

Answer 6

oh, got it.
but I am stuck at:
√2 cos x = √6 sin x
cos x = √3 sin x
am I right so far?

the the answer is 30° & 210°

Answer 7

Ok !
You get :
\[\sqrt3\sin x=\cos x\]
bu dividing over cos x we get :
\[\sqrt3\tan x=1\]
then :
\[\tan x=\frac1{\sqrt3}\]
That means :
\[x=30^\circ\]

Answer 8

wao, I wish I am as smart as you! I couldn't see that "far".
Thank you so much again!!

Answer 9

There is no need to be smart to solve that type of exercises ! :)
It needs only to know the formulas !
That's all !
Anyway, you are welcome !