Question

solve 4 sin^3 x + 2 sin^2 - 2 sin x -1 =0

Answer 1

4sin^(3)x+2sin^(2)x-2sinx-1=0

Factor the polynomial by grouping the first two terms together and finding the greatest common factor (GCF). Next, group the second two terms together and find the GCF. Since both groups contain the factor (2sinx+1), they can be combined.
(2sin^(2)x-1)(2sinx+1)=0

2sin^(2)x-1=0 and 2sinx+1=0
sin^2 x=1/2 and sinx=-1/2

Answer 2

did you get x = 60 and x = 270

Answer 3

\[\sin^2 x=1/2 \] and\[ sinx=-1/2\]
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\[\sin^2 x=1/2 \]
\[\sin(x)=\frac{\sqrt{2}}{2}\]
x=45,135
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\[ sinx=-1/2\]
x=30,150,330