If sin3θ.sec6θ = 1 then find the value of 3tan23θ?1. 12. 23. 54. 7

1.	If sin3θ.sec6θ = 1 then find the value of 3tan23θ?1. 12. 23. 54. 7
Answer» Correct Answer - Option 1 : 1 Given: It is given that sin3θ.sec6θ = 1 Formula Used: Basic concept of trigonometric ratio and identities We know that Secθ = 1/cosθ Cos(90 - θ) = sin θ tan30° = 1/√3 Calculation: As we know that reciprocal of secθ is equal to cosθ ∴ Sin3θ/cos6θ = 1 ⇒ sin3θ = cos6θ ∵ Cos(90 - θ) = sin θ ∴ sin3θ = sin(90 - 6θ) ⇒ 3θ = 90 - 6θ ⇒ θ = 10° Now, 3tan²3θ ∴ 3tan²3θ = 3tan²30° = 3 × (1/√3)² = 1 Hence, option (1) is correct

Answer» Correct Answer - Option 1 : 1

Given:

It is given that sin3θ.sec6θ = 1

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Secθ = 1/cosθ

Cos(90 - θ) = sin θ

tan30° = 1/√3

Calculation:

As we know that reciprocal of secθ is equal to cosθ

∴ Sin3θ/cos6θ = 1

⇒ sin3θ = cos6θ

∵ Cos(90 - θ) = sin θ

∴ sin3θ = sin(90 - 6θ)

⇒ 3θ = 90 - 6θ

⇒ θ = 10°

Now, 3tan²3θ

∴ 3tan²3θ = 3tan²30° = 3 × (1/√3)² = 1

Hence, option (1) is correct

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