Question

hey guys............

Here is my question........

Find number of solutions of this trigonometric equation in the range - 2pi < thita < 2pi

Answer 1

Given,

sin∅ + sin7∅ = sin4∅

sin7∅ + sin∅ = sin4∅

2sin(∅+7∅)/2 cos(7∅-∅)/2 = sin4∅

2sin4∅ * cos3∅ = sin4∅

cos3∅ = 1/2

cos3∅ = cosπ/3

3∅= 2nπ $\frac{+}{}$ π/3

-ve (n=1)

3∅ =5π/3

∅= 5π/9

or,

∅= π/9