SOLUTION: Please help me with this equation: {{{ 2(cos(x))^2=1-sin(x) }}} So far I've gotten down to {{{ 2-2(sin(x))^2+sin(x)-1=0 }}} but I don't know what to do from here.

Question 1027244: Please help me with this equation:
So far I've gotten down to but I don't know what to do from here.
Answer by ikleyn(52909) (Show Source): You can put this solution on YOUR website!
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Please help me with this equation:
So far I've gotten down to but I don't know what to do from here.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 = ,

 = ,       (It is what your got, and it is correct !)

Next introduce new variable t = sin(x) for shortness. You will get

 = ,

 = .

Solve this quadratic by applying the quadratic fotmula 

 =  = .


One root is   = 1  --->  sin(x) = 1  --->  x = ,  k = 0, +/-1, +/-2, . . . 


The other root is   =   --->  sin(x) =   --->  x = ,  k = 0, +/-1, +/-2, . . .

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