If (1+sinθ – cosθ)/(1+sinθ+cosθ) + (1+sinθ+cosθ)/(1+sinθ-cosθ) = 4, then which of the following values will be suitable for θ ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 30o
We have given that,
⇒ (1+sinθ – cosθ)/(1+sinθ+cosθ) + (1+sinθ+cosθ)/(1+sinθ-cosθ) = 4
We can't use any identity here to simplify the given set of problems so we will use basic algebraic operations.
⇒ {(1+sinθ – cosθ)2 + (1+sinθ+cosθ)2}/(1+sinθ-cosθ)(1+sinθ-cosθ) = 4
⇒ 2{1 + sin2θ + 2sinθ + cos2θ}/(1+sinθ-cosθ)(1+sinθ-cosθ) = 4
⇒ 4{1 + sinθ}/(1 + sin2θ + 2sinθ - cos2θ) = 4
⇒ 1 + sinθ = 1 + sin2θ + 2sinθ - 1 + sin2θ
⇒ 2sin2θ + sinθ - 1 = 0
⇒ (sinθ - 1)(2sinθ - 1) = 0
Here sin cannot be negative so
⇒ 2sinθ = 1
⇒ sinθ = 1 / 2
⇒ θ = 30o