Question

solve 2cos^2x-sinx=1, 0 < or equal to x < 2pie

Answer 1

cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )


2 cos ^ 2 ( x ) - sin ( x ) = 1

2 * [ 1 - sin ^ 2 ( x ) ] - sin ( x ) = 1

2 - 2 sin ^ 2 ( x ) - sin ( x ) = 1 Subtract 1 to both sides

2 - 2 sin ^ 2 ( x ) - sin ( x ) - 1 = 1 - 1

- 2 sin ^ 2 ( x ) - sin ( x ) + 1 = 0


Substitute :

sin ( x ) = u


- 2 u ^ 2 - u + 1 = 0


The exact solution are :

u = 1 / 2

u = - 1


cos ( x ) = 1 / 2

cos ( x ) = - 1



x = 30 ° = pi / 6

x = 270 ° = 9 pi / 6 rad



P.S

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- 2 u ^ 2 - u + 1 = 0

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- 2 u ^ 2 - u + 1 = 0

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Answer 2

Corection:

sin ( x ) = 1 / 2

sin ( x ) = - 1

Answer 3

would the 3 answers be: pi/6, 5pi/6, 3pi/2

Answer 4

Yes