If sin a= , then find the value of (3 cos a -4 cos³ a).

Question :If sin a= , then find the value of (3 cos a -4 cos³ a).

The correct answer :We have been given that sin A = 1/2. From this, we will find the value of A.

⇒ A =  (1/2)

⇒ A = π/6

Now, cos A = cos π/6 = √3/2

Hence, 3cosA = (3√3)/2

cos³A = ( √3/2 )³ = (3√3)/8

⇒ 4cos³A = 4 x (3√3)/8 = (3√3)/2

Substituting these values we get

3 cos A – 4cos³A = (3√3)/2 – (3√3)/2 = 0

∴ L.H.S. = R.H.S.