Question

If α and β are complementary angles then find the value of cot12β if sinα = cos(4β - 15)?
1. 1/√3
2. √3
3. 1
4. 0

Answer 1

Correct Answer - Option 1 : 1/√3

Given:

It is given that α and β are complementary angles and sinα = cos(4β - 15)

Formula Used:

Basic concept of trigonometric ratio and identities

We know that

Sin(90 - θ) = cosθ

Cot 60° = 1/√3

Calculation:

α and β are complementary angles

∴ α + β = 90°

⇒ α = 90° - β

Now, sinα = cos(4β - 15)

∴ sin(90° - β) = cos(4β - 15)

⇒ cosβ = cos(4β - 15)

⇒ β = 5°

Now, we have to find the value of cot12β = cot(12° × 5) = cot 60° = 1/√3

Hence, option (1) is correct