Question

`f(x) = 1 - cos (2x) - sin^2 x` and `f(x) = a + b cos (cx)` How to determine a, b & c ?

I canwrite this to cos^x - cos(2x).
And I can see that c, should be 2. Because of the (2x)
So we got f(x) = a + b cos (2x)

a and b are ??

Answer 1

Given
`f(x) = 1 - cos (2x) - sin^2 x` and
`f(x) = a + b cos (cx)`
So
`f(x) = 1 - cos (2x) - sin^2 x`

`=>f(x) = cos^2x - cos (2x)`

`=>f(x) = 1/2(1+cos2x) - cos (2x)`

`=>f(x) = 1/2+1/2cos2x - cos (2x)`

`=>f(x) = 1/2-1/2cos2x`

Comparing this with `f(x) = a + b cos (cx)`

we can write

`a=1/2,b--1/2and c=2`