Question

Solve the following equation:
sin2x + sinx = 0

Please help!​

Answer 1

x = 0, π,2π

Explanation:

Given:

sin 2x+sin x=0

• we have Sin 2x= 2sinx cosx

2sinx cosx +sin x =0

Taking common sin x.

Sin x( 2cos x+1)=0

either

sinx = 0

or

2cosx + 1 = 0

If sinx = 0, then x = 0, π, or 2π.

If 2cosx + 1 = 0, then

cosx = -1/2.

x = cos (180-60)=cos 120 =-1/2

The cosine of 60 degrees is negative in quadrant 2.

In terms of π

`x = (2)/(3)\pi`

Therefore,

The value of x is 0, π,2π or
`(2)/(3)\pi`