Question

If 2 cos theta = underoot 3 , prove that 3 sin theta - 4 sin^3 theta = 1.

Answer 1

Answer:

Step-by-step explanation:

2 Cosθ = √3

=> Cosθ = √3/2

=> θ = 30°

Now 3 sinθ - 4 sin³θ

= Sin3(30°)  (∵Sin3θ = 3Sinθ - 4Sin³θ)

= Sin90°

= 1

= R.H.S

Hence proved

Answer 2

Answer:

Step-by-step explanation:

We have,

• 2 cos Ф = √3

So,

• cos Ф = √3/2

We know,

⇒ cos 30° = √3/2

∴ Ф = 30°

So,

• 3 sin Ф - 4 sin³ Ф = 1

We know,

• sin 3 Ф = 3 Sin Ф - 4 Sin³ Ф

Hence,

⇒ sin (3 × 30)°

⇒ sin 90°

• 1

∴ L.H.S = R.H.S