Question

Sinθ = 2/√5, where 90° < θ < 180°, then find the value of Cosθ/Cotθ + Tanθ/Cosecθ

1. 2/√5
2. 1/√5
3. –2/√5
4. –1/√5

Answer 1

Correct Answer - Option 3 : –2/√5

Given:

Sinθ = 2/√5

90° < θ < 180°

Concept used:

Sinθ = P/H = 1/Cosecθ

Cosθ = B/H = 1/Secθ

Tanθ = P/B = 1/Cotθ

Where P = perpendicular, B = base, H = hypotenuse

Calculation:

H² = P² + B²

⇒ 5 = 4 + B²

⇒ B = 1

Cosθ/Cotθ + Tanθ/Cosecθ

⇒ \(\frac{{ - \;\frac{1}{{√ 5 \;}}}}{{ - \;\frac{1}{2}}} + \;\frac{{( - \;2)}}{{\frac{{√ 5 }}{2}}}\) [θ is in second quadrant]

⇒ 2/√5 – 4/√5

⇒ (2 – 4)/√5

⇒ –2/√5

∴ Required value is –2/√5.