Question

Show that Cos 6x = 32 Cos6 x – 48 Cos4 x + 8 cos2 x - 1

Answer 1

Step-by-step explanation:

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

Answer 2

Answer:

LHS = cos6x

= cos3(2x)

use, the formula,

cos3A = 4cos³A - 3cosA

= 4cos³(2x) - 3cos(2x)

use the formula,

cos2A = 2cos²A -1

= 4(2cos²x-1)³ - 3(2cos²x-1)

= 4{8cos^6x -3.(2cos²x)².1 +3.2cos²x.1² - 1 }-6cos²x +3

= 32cos^6x -48cos⁴x + 24cos²x -4 -6cos²x + 3

= 32cos^6x - 48cos⁴x +18cos²x -1 = RHS

Step-by-step explanation: