Use the double angle formulae and the identity cos(A+B)≡cos(A)cos(B)−sin(A)sin(B) to obtain an expression for cos 3x in terms of cos x only

To answer, you need to know and be able to use your trigonometric formulae including the double angle formulae on data sheet.

1: cos(3x)=cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x)        split the 3x into two terms, 2x and x

2: Using trig identity cos(2A)=2cos^2(x) - 1   and  sin(2A)=2sinAcosA

cos(2x)cos(x) - sin(2x)sin(x) = [2cos^2(x) - 1]cos(x) - [2sin(x)cos(x)]sin(x)

3: expand out

2cos^3(x) - cos(x) - 2[sin^2(x)]cos(x)

4: use trig identity sin^2(x)=1 - cos^2(x)

2cos^3(x) - cos(x) - 2cos(x)[1 - cos^2(x)]

5: simplify

Answer = 4cos^3(x) - 3cos(x)