If 3Sec2θ + Tanθ = 7, 0o < θ < 90o, then the value of (Cosec2θ + Cosθ)/(Sin2θ + Cotθ) is:
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. (2 + √2)/4
⇒ 3sec2θ + Tanθ = 7
We know that,
⇒ 1 + Tan2θ = Sec2θ
By putting the value of Sec2θ in the equation
⇒ 3(1 + Tan2θ) + Tanθ = 7
⇒ 3 + 3Tan2θ + Tanθ = 7
⇒ 3Tan2θ + Tanθ - 4 = 0
⇒ (Tanθ - 1)(Tanθ + 4/3) = 0
⇒ Tanθ = 1
⇒ θ = 45o
⇒ (Cosec2θ + Cosθ)/(Sin2θ + Cotθ)
⇒ (Cosec90o + Cos450)/(Sin90o + Cot45o)
⇒ (1 + 1/√2)/(1 + 1)
⇒ ((√2) + 1)/(2√2)
By rationalization,
⇒ ((√2) + 1)/(2√2) × (2√2)/(2√2)
⇒ (4 + 2√2)/8
⇒ (2 + √2)/4