Help solving by using trig identity

[MacFanBoy]

Homework Statement

sinx cos2x=1

x is greater than or equal to 0 and less than 2pi

Homework Equations

What I used:
1-2sin²x
cos²x-sin²x

but there might be one that I didn't and should have...

The Attempt at a Solution

Basically I have substituted to the point that I can, I feel pretty bad since this is a review..

sinx cos2x=1

sinx (1-2sin²x)=1

basically didn't know where to go from there..

and

sin cosx=1
sinx (cos²x-sin²x)=1
sinx(cos²x)-sin³x=1
sinx(1-sin²x)-sin³x=1

sinx-sin³x-sin³x=1

And that one stopped there...
we are supposed to only use trigonometric identities, nothing more nothing less; and once again I don't understand how I can not get this since it is a review..

Thanks

 

[Mentallic]

sinx-sin3x-sin3x=1

Yes can you see how this is a cubic function in sinx?
Maybe if you rearranged it, it will become more clear.

 

[matt_crouch]

sinx (1-sin²x)=1

try multiplying out the brackets and rearranging the equation so that its =0 from there you should get a quadratic equation.

 

[HallsofIvy]

Well, you get a cubic equation as Mentallic said. Fortunately one that is easy to solve.

 

[MacFanBoy]

Haha, wow surprised I didn't see that one, thanks guys!