Question

If 4θ is an acute angle, and cot 4θ = tan (θ - 5°)  , then what is the value of θ?
1. 24°
2. 45°
3. 21°
4. 19°

Answer 1

Correct Answer - Option 4 : 19°

Given:

4θ is an acute angle,

And cot 4θ = tan (θ - 5°).

Formula used:

tan (90° - θ) = cot θ 

Calculation:

cot 4θ = tan (θ -5°)

⇒ tan (90° - 4θ) = tan (θ -5°)

⇒ 90° - 4θ = θ -5° 

⇒ 90° + 5° = θ + 4θ 

⇒ 95° = 5θ 

⇒ θ = 19° 

∴ the value of θ is 19°.