If 2 sin Θ + 15 cos2 Θ = 7 , 0° < Θ < 90° then what is the value of (3 - tanΘ)/(2 + tanΘ)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1/2
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2sinΘ + 15cos2Θ = 7 2sinΘ + 15(1- sin2Θ) - 7 = 0 15 sin2Θ - 2 sinΘ - 8 = 0 15sin2Θ + 10 sinΘ - 12sinΘ - 8 = 0 (3 sinΘ - 2)(5 sinΘ - 4) = 0 sin Θ = 4/5 , sin Θ = -2/3 so the valid sin Θ = 4/5 So, cosΘ = 3/4 and tanΘ = 4/3 Hence (3 - tanΘ)/(2 + tanΘ) = (3 - 4/3)/(2 + 4/3) = 5/10 = 1/2
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