Question

If sin 3θ ⋅ sec 6θ = 1 then find the value of 3 tan² 3θ?
1. 1
2. 2
3. 5
4. 7
5. 4

Answer 1

Correct Answer - Option 1 : 1

Given:

It is given that sin 3θ ⋅ sec 6θ = 1

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Sec θ = 1/cos θ

Cos(90 - θ) = sin θ

tan 30° = 1/√3

Calculation:

As we know that reciprocal of secθ is equal to cosθ

∴ Sin 3θ/cos 6θ = 1

⇒ sin 3θ = cos 6θ

∵ Cos(90 - θ) = sin θ

∴ sin 3θ = sin(90 - 6θ)

⇒ 3θ = 90 - 6θ

⇒ θ = 10°

Now, 3 tan² 3θ

∴ 3 tan² 3θ = 3 tan² 30° = 3 × (1/√3)² = 1

Hence, option (1) is correct