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=$\frac{-1}{2}$

x=$\frac{\pi}{2}$ or multiples of $\frac{\pi}{2}$

x=$\frac{2\pi}{3}$ or multiples of $\frac{2\pi}{3}$

x=$\frac{-2\pi}{3}$ or multiples of $\frac{-2\pi}{3}$