If 
= 4sec θ, 0° < θ < 90°, then the value of cotθ + cosec θ is :
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. √3
1/1+sinθ × (1 - sinθ/1 -sinθ ) + 1/1 - sinθ × (1 + sinθ/1 + sinθ)
(1 + sinθ /1 – sin2θ) + (1 – sinθ /1 – sin2θ) = 4secθ
(1 + sinθ /cos2θ) + (1 – sinθ /cos2θ) = 4secθ
(1 + sinθ + 1 – sinθ)/cos2 θ = 4secθ
2/cos2θ = 4secθ
2sec2θ = 4secθ
secθ = 2
θ = 60°
cotθ + cosecθ = cot60° + cosec60°
cotθ + cosecθ = (1/√3) + (2/√3)
cotθ + cosecθ = 3/√3 = √3