If 3 + cos2θ = 3(cot2θ + sin2θ), 0° < θ < 90°, then what is the value of (cosθ + 2sinθ)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. (2√3 + 1)/2
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Understanding |
Application |
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3 + cos2θ = 3(cot2θ + sin2θ), 0° < θ < 90° |
3 + cos2θ = 3(cot2θ + sin2θ) ⇒ 3 + cos2θ = 3cot2θ + 3(1 – cos2θ) ⇒ 3 + cos2θ = 3cot2θ + 3 – 3cos2θ ⇒ 4cos2θ = 3(cos2θ/sin2θ) ⇒ sin2θ = 3/4 ⇒ sinθ = √3/2 ⇒ sinθ = sin60° So, θ = 60° |
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We need to put θ = 60° in the given expression: (cos θ + 2sinθ) |
So, (cos60° + 2sin60°) = 1/2 + 2√3/2 = (2√3 + 1)/2 |