Question

If cosec θ = \(\frac{41}{9}\) and θ is an acute angle, then the value of 5 tan θ will be:
1. \(\frac{7}{8}\)
2. \(\frac{9}{8}\)
3. \(\frac{11}{8}\)
4. \(\frac{13}{4}\)

Answer 1

Correct Answer - Option 2 : \(\frac{9}{8}\)

Given:

cosec θ = \(\frac{41}{9}\) 

Formula:

sin²θ + cos²θ = 1

Calculation:

sin θ = 9/41

cos θ = √(1 - (9/41)²) = 40/41

tan θ = (sinθ)/(cosθ) = (9/41) × (41/40) = 9/40

∴ 5 tanθ = 5 × 9/40 = 9/8