Question

f θ = 30°, verify that cos 3θ = 4 cos³ θ − 3 cos θ

Answer 1

Given:

θ = 30° ......(1)

To verify

cos 3θ = 4 cos³ θ − 3 cos θ    .....(2)

Now consider left-hand side of the expression in equation (2)

Therefore

`cos 3theta = cos 3 xx 30`

 = cos 90

= 0

Now consider right hand side of the expression to be verified in equation (2)

Therefore

`4cos^3 theta - 3 cos theta = 4cos^3 30 - 3 cos 30`

`= 4 xx (sqrt3/2)^3 - 3 xx (sqrt3/2)`

`= (3sqrt3)/3 = (3sqrt3)/2`

= 0

Hence it is verified that,

`cos 3theta = 4cos^3 theta - 3 cos theta`