Question

Find the least positive angle measured in degrees satisfying the equation sin cube x + sin cube 2 x + sin cube 3 X equal to sin x + sin 2x + sin 3x whole cube

Answer 1

0 degree may be the correct answee

Answer 2

Let sinx=a, sin2x=b, and sin3x=c

Expand out

(a+b+c)^ 3

Then subtract a^3,b^3 and c^3, which yields

3a^2b+3a^2c+3ab^2+6abc+3ac^2+3b^2c +3bc^2=0

The long expression can be factored nicely into :

3(a+b)(b+c)(a+c), which equal to 0.

The factor 3 makes no difference, so solve for:

sin(x)+sin(2x)=0 ,

sin(2x)+sin(3x)=0, and

sin(x)+sin(3x)=0,