SOLUTION: solve the equation: 6cos^2(x)+8sin(x)=cos(2x)

As a first step, express all terms via sin(x):

 = ,

 =  =  = .

Now substitute them into the original equation:

 +  = {{1-2sin^2(x)}}}.

Simplify:

 = .

Apply the quadratic formula:

 =  = .

Of the two values only sin(x) =  is acceptable.

Thus  the solutions are  x =   and/or  x = .