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