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

YEEEEEET Feb 3, 2019

#1**+2 **

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

CPhill Feb 3, 2019