for this one i tried dividing everything by sin0 but the 1 just got in the way of the method, im not sure what rule i should use for this one please help thanks
1 + sin xcos^2x = sinx
We need to be careful about dividing through by a trig function, YEEEEEET...we might be throwing away a possible solution!!!
We can wrtite this as
1 + sin x ( 1 - sin ^2 x) = sin x
1 +sin x - sin ^3 x = sin x
1 - sin^3 x = 0
sin^3x - 1 = 0 factor as a difference of cubes
(sin x - 1) (sin^2x + sin x + 1) = 0
The second factor produces no real solutions for x
For the first factor
sin x - 1 = 0
sin x = 1
And this happens when x = 90°
The graph here confirms this
https://www.desmos.com/calculator/lljppoztzo