If 2 sinθ + 15 cos2θ = 7, 0o < θ < 90o, then tanθ + cosθ + secθ =
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Correct answer: A
Explanation
The correct answer is option 1 i.e 18/5.
2 sinθ + 15cos2θ = 7
2 sinθ + 15(1 - sin2θ) = 7
2 sinθ + 15 - 15 sin2θ = 7
15sin2θ - 2 sinθ - 8 = 0
sin2θ - (2sinθ)/15 - 8/15 = 0
sin2θ + (2sinθ)/3 - (4sinθ)/5 - 8/15 = 0
sinθ(sinθ + 2/3) - 4/5(sinθ + 2/3) = 0
(sinθ - 4/5) (sinθ + 2/3) = 0
For 0o < θ < 90o,
sinθ = 4/5
Perpendicular = 4
Hypotenuses = 5
By triplet 3-4-5,
Base = 3
Now,
tanθ + cosθ + secθ
= 4/3 + 3/5 + 5/3
= 54/15 = 18/5