If cotθ = 4/3, then evaluate (secθ(1 + cot2θ)(cosec2θ − cot2θ))/ cosec3θ.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 3/4.
(secθ(1 + cot2θ)(cosec2θ − cot2θ))/cosec3θ
⇒ (secθ × cosec2θ × 1)/cosec3θ
⇒ secθ/cosecθ
⇒ (1/cosθ)/(1/sinθ)
⇒ sinθ/cosθ = tanθ
Given that, cotθ = 4/3 then,
⇒ tanθ = 3/4 [tanθ = 1/cotθ]