Question

Solve for x: sinx + sin2x + sin3x = 0​

Answer 1

Step-by-step explanation:Use trig identity:sina+sinb=2sin(a+b2).cos(a−b2) In this case:sinx+sin3x=2sin(2x).cos(x) (sinx+sin3x)+sin2x=2sin(2x)cos(x)+sin(2x)==sin(2x)(2cosx+1)=0 Either one of the 2 factors must be zero.a. sin 2x = 02x = 0 --> x = 02x=π --> x=π2 2x=2π --> x=π General answer: x=kπ2 b. 2cos x + 1 = 0 --> cosx=−12 Trig table and unit circle give 2 solutions -->x=±2π3+2kπ

hope it's helpful please support me