Question

20. Prove that cos6x = 32cos6

x – 48cos4

x + 18cos2

x - 1​

Answer 1

Using,

cos2x=2cos

2

x−1

cos3x=4cos

3

x−3cosx

LHS:

cos6x=2cos

2

3x−1

=2(4cos

3

x−3cosx)

2

−1

=2(16cos

6

x+9cos

2

x−24cos

4

x)−1

=32cos

6

x−48cos

4

x+18cos

2

x−1 = RHS