If cos θ = 2p/(p2+ 1), (p≠±1) then cosec θ is equal to:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. (p2+1)/(p2– 1)
|
Concept |
Understanding |
Application |
Fair calculation |
|
Cos x = base/ hypotenuses Cosec x = hypotenuses/perpendicular Pythagoras theorem Base2 = Hypotenuses2 – Perpendicular2 |
Given Cos θ = 2p/(p2 + 1) By comparing base = 2p Hypotenuses = (p2+1)
|
Perpendicular2 = Hypotenuses2 – Base2 Perpendicular = (p2– 1) Hence, Cosecθ = (p2+1)/(p2– 1) |
Perpendicular2 = (p2+1)2 - (2p)2 = p4 + 1 + 2p2 – 4p2 = p4 + 1 - 2p2 = (p2– 1)2 So, Perpendicular = (p2– 1) |