# Answer to Question #16549 in Trigonometry for Billy

Question #16549

what is cos^2 - sin^2 = 1 - sin

and

9 + 9sin = 6cos^2

and

9 + 9sin = 6cos^2

Expert's answer

1) -sin^2x+sinx=sin^2x => 2sinx=1 => sinx=1/2 => x=pi/3+2pi*k or

2pi/3+2pi*k, k from Z

2) 3+3sinx=2cos^2x =>2-2cos^2x=-1-3sinx =>

2sin^2x+3sinx+1=0 => sinx=-1 or sinx=-1/2 => x=-pi/2 + 2pi*k, or

x=-pi/3+2pi*k or x=-2pi/3+2pi*k

2pi/3+2pi*k, k from Z

2) 3+3sinx=2cos^2x =>2-2cos^2x=-1-3sinx =>

2sin^2x+3sinx+1=0 => sinx=-1 or sinx=-1/2 => x=-pi/2 + 2pi*k, or

x=-pi/3+2pi*k or x=-2pi/3+2pi*k

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