If 2sinϴ + 15cos2ϴ = 7, 0 < ? < 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)
2sinϴ + 15cos2ϴ = 7
⇒ 2sinϴ + 15(1 - sin2ϴ) = 7
⇒ 15 sin2ϴ - 2sinϴ - 8 = 0
⇒ sinϴ = 4/5 or -2/3
as, 0 < ϴ < 90
⇒ sinϴ = 4/5 ⇒ cosϴ = 3/5
so, tanϴ = 4/3
(3 - tanϴ)/(2 + tanϴ) = (3 - 4/3)/(2 + 4/3) = 5/10 = 1/2