If 4 sin2 θ = 1 and θ is an acute angle, then the value of cos2θ + tan2θ is:
\(13\over12\)
The correct answer is Option 1 i.e. \(13\over12\).
4 sin2 θ = 1
⇒ sin2θ = 1/4
⇒ sinθ = 1/2 = P/H
By Pythagoras' theorem,
⇒ H2 = B2 + P2
here, H = Hypotaneous, B = Base, P = Perpendicular
⇒ B2 = 22 - 12
⇒ B2 = 4 - 1
⇒ B = \(\sqrt3\)
The value of cos2θ + tan2θ
⇒ (\(\sqrt3\)/2)2 + (1/\(\sqrt3\))2
⇒ 3/4 + 1/3
⇒ (9 + 4)/12 = \(13\over12\)
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