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avatar+838 

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

 Feb 3, 2019
 #1
avatar+100439 
+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

 

 

 

cool cool cool

 Feb 3, 2019
 #2
avatar+838 
+1

got it! thanks so much

YEEEEEET  Feb 3, 2019
edited by YEEEEEET  Feb 3, 2019

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