Question

If sin A =1/2 then prove 3 cos A- 4 cos^3A=0

Answer 1

Answer:

Step-by-step explanation:

by this right angled triangle

we have,

sinA=1/2

cosA=√3/2

so cos^3(A) = 3√3/8

substituting these values we get

3cosA-4cos^3(A)

= 3*√3/2–4*3√3/8

=(3√3/2) – (3√3/2)

= 0

And hence it is proved

Hope this helps u

Answer 2

The proof of 3cos A - 4cos³A = 0 is given below.

Given:

sin A =1/2

To Find:

Proof of 3 cos A- 4 cos³A=0

Solution:

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

⇒ A = $sin^{-1}$ (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.

Hence Proved.

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