Question -
Answer -
It is given that
sin x + sin 3x + sin 5x = 0
We can write it as
(sin x + sin 5x) + sin 3x = 0
Using the formula
By further calculation
2 sin 3x cos (-2x) +sin 3x = 0
It can be written as
2 sin 3x cos 2x + sin3x = 0
By taking out thecommon terms
sin 3x (2 cos 2x + 1)= 0
Here
sin 3x = 0 or 2 cos 2x+ 1 = 0
If sin 3x = 0
3x = n╧А, where n тИИ Z
We get
x = n╧А/3, where n тИИ Z
If 2 cos 2x + 1 = 0
cos 2x = тАУ 1/2
By furthersimplification
= тАУ cos ╧А/3
= cos (╧А тАУ ╧А/3)
So we get
cos 2x = cos 2╧А/3
Here
