Question 775359: find all exact solutions to the equation on [0,2 pi): 2 sin^2u= 1-sinu
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! First move all the terms to LHS:
2sin^2(u) + sin(u) - 1 = 0
If we let x=sin(u), this gives
2x^2 + x - 1 = 0
This can be factored as (2x-1)(x+1) = 0
This gives x = 1/2, x = -1, or sin(u) = 1/2, sin(u) = -1
(Or we could have completed the factoring in terms of sin(u) directly)
I'll leave it as an exercise for you to determine the values of u.
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