Solve cos2xsinx=1: Simplifying and Finding X

[CutiePieYum]

Homework Statement

Simplify AND Solve for X
cos2xsinx=1

Homework Equations

The triples, doubles

The Attempt at a Solution

cos2xsinx=1
(cos^2x-sin^2x)(sinx)=1
(-1x)(sinx)=1
-sinx=1
sinx= -1
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:-/

Help.. :)

 

[Dick]

The maximum absolute value of cos(2x) and sin(x) is 1. So the only way you can solve that is if cos(2x)=1 AND sin(x)=1 or cos(2x)=(-1) AND sin(x)=(-1). Is either of those possible? If so which one?

 

[CutiePieYum]

I have no idea may i have another clue

 

[CutiePieYum]

anyone?

 

[Dick]

I have no idea may i have another clue

Graph cos(2x) and sin(x) on [0,2pi]. Or do this cos^2(x)-sin^2(x)=1-2*sin^2(x). So you have (1-2*sin^2(x))*sin(x)=1. If sin(x)=u then you have (1-2*u^2)*u=1. That's a cubic equation for u. Can you find the real root?