Option 1 : 1

Electric charges and coulomb's law (Basic)

42773

10 Questions
10 Marks
10 Mins

**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 tan^{2 }3θ

∴ 3 tan^{2 }3θ = 3 tan^{2 }30° = 3 × (1/√3)^{2} = 1

**Hence, option (1) is correct**