Question

If 4θ is an acute angle, and cot 4θ = tan (θ - 5°) , then what is the value of θ?

• A. 24°
• B. 45°
• C. 21°
• D. 19°

Answer 1

Answer:

D. 19°

Solution: 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°.