Question

What are the exact solutions of sin2x+sinx-2cox-1=0?

Answer 1

sin2x+sinx-2cox-1=0

As we know, Sin 2x =2sinx cosx

2Sinx Cosx+Sinx-2cosx-1=0

Sinx(2cos x+1)-1(2cosx+1)=0

(sinx-1)(2cosx+1)=0

So, either sinx-1=0 or 2cos x+1=0

Sin x=1 or cos x=
`(-1)/(2)`

x=
`(\pi)/(2)` or multiples of
`(\pi)/(2)`

x=
`(2\pi)/(3)` or multiples of
`(2\pi)/(3)`

x=
`(-2\pi)/(3)` or multiples of
`(-2\pi)/(3)`