How to eliminate theta?

Question

xcos(3θ) + ysin(3θ) = bcos(θ)

xsin(3θ) + ycos(3θ) = bcos(θ + π/6)

 

How to eliminate theta between these pair of equations?

Answer 1

The following identities will get you equations in which the 3 coefficient has been eliminated from the angle

3x = 3 sin x - 4 sin³x

and

cos 3x = 4 cos³x - 3 cos x

That may allow you to solve for the angle theta.

P.S.

I agree with Kenneth's correction of your grammar!