What is the angle that maximizes R?

[TN17]

Homework Statement

Sorry for the long intro:

An object is propelled up at angle theta 45 deg. < theta < 90 deg. to the horiz. with initial vel. of V0 m/s. from the base of a plane that makes an angle of 45 deg. with the horiz.
If air resistance is ingored, the distance, R, traveled by the object up the inclined plane, is
R = V^2(sqrt 2)/ 32 (2sinthetacostheta - 2cos^2theta

Question
You are asked to find the angle that maximizes R by solving equation
2sinthetacostheta + 1 - 2sin^2theta = 0
Solve for theta.

Homework Equations

Not really any equations, just solving.

The Attempt at a Solution

I tried to continue with this, but I don't know what to do when there are two different identities.

Would I factor?

 

[Mentallic]

Do you know what sin(2x) and cos(2x) equal in terms of cosx and sinx?

 

[TN17]

Do you know what sin(2x) and cos(2x) equal in terms of cosx and sinx?

Well, sin(2x) = 2sinxcosx
and cos(2x) = 2cos^x - sin^2x or 2cos^2x - 1 or 1- 2sin^2x
Is that what you mean?

 

[Mentallic]

Yes, so do you see how you can change your equation in terms of sin(2x) and cos(2x)?

Now how would you go about solving something like sin(2x)=cos(2x)
You don't need to worry about the 2x for the moment, you can just think of it as any other variable angle.