If sec θ – tan θ = P, then cosec θ = ?
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 
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Understanding |
Application |
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Given: Secθ – Tanθ = P |
Sec2θ – Tan2θ = 1 ⇒ (Secθ – Tanθ) (Secθ + Tanθ) = 1 Since, Secθ – Tanθ = P ⇒ (Secθ + Tanθ) = 1/P Adding both equations: ⇒ Secθ = (P + 1/P)/2 ⇒ Secθ = (P2 + 1)/2P So, Cosθ = 2P/(P2 + 1) = Base/Hypotenuse Hence, Perpendicular = (1 – P2) Cosecθ = Hypotenuse/Perpendicular = (P2 + 1)/(1 – P2) |