We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

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