Trig simplification (this one is tough)
f(x)= (4cos (x) -cos (3x))^2 + (3sin (x) -sin (3x))^2
f(x) has to be simplified to the form: f(x)= a cos ^2 (2x) + b cos (2x) + c where a,b,and c are real numbers.
so far I expanded the two parentheticals to: f(x)= 16 cos ^2 (x) - 8 cos(x) cos(3x) + cos ^2 (3x) + 9 sin^2 (x) -6 sin (x) sin (3x) + sin ^2 (3x)
after this I'm stumped.
I tried merging the 16cos ^2 (x) + sin ^2 (3x) to a 7 cos ^2(x) + 9, and doing the same with the sin ^2 (3x) + cos ^2 (3x) = 1. But it isn't taking me anywhere.
If someone can solve this with work, I would highly appreciate it!