Trigonometric Functionssimplify sin squared functions

[ku1005]

just looking at another question to do with trigonometric functions and I can't see how they simplify the follwing:
2sin^2x-3sinx-2=0 to
(2sinx+1)(sinx-2)=0
again i prob thinking sumthin really stupid...but i can't see wat! cheers

 

[steve23063]

The equation can be treated like a normal quadratic equation.

use substitution and replace "sinx" with "x"
2(sinx)^2-3sinx-2=0 ----> 2x^2-3x-2=0

factor the equation
2x^2-3x-2=0 = (2x+1)(x-2)

Replace "x" with "sinx"
(2x+1)(x-2)=0 -----> (2sinx+1)(sinx-2)=0


If you aren't allowed to use this method and you have to use trig identities then someone else will have to help. I'm too lazy to look up or derive the identities right now

 

[ku1005]

cheers mate...and i like ur thinkin! LOL