Trigonometric Equation with Multiple Functions and Arguments

[Islwyn]

Can anyone help solve the below for 'a'

0=b(ycos(a)-bcos(2a)+xsin(a))

I've reduced it to

b=ycos(a)+2sin(a)sin(a)+xsin(a)

=sin(a)(cot(a)+2sin(a)+x)

Which I think is right, but I can't get any further without just ending up with different forms that appear more complex.

 

[quantumdude]

What makes this equation tough is the fact that you've got 2 different trig functions running around there. What's more you've got 2 different arguments in your cosine functions. I would try to express everything in terms of $\cos(a)$, so that you end up with a polynomial equation in that quantity.

Try to make use of the following identities:

$$\cos(2a)=2\cos^2(a)-1$$

$$\sin(a)=\sqrt{1-\cos^2(a)}$$

I don't think you're going to get a closed form expression for a, but if you have numerical values for the parameters you will be able to get approximate solutions.