Question
Download Solution PDFIf 4 sin2θ = 3 (1 + cos θ), 0° < θ < 90°, then what is the value of \(\rm \sqrt{15}\tan \theta+\frac{4}{\sqrt{15}}\sin \theta+2\sec \theta\)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
4 sin2θ = 3 (1 + cos θ).
Formulas used:
sin2θ = 1 - cos2θ
tanθ = sinθ / cosθ
secθ = 1 / cosθ
Calculation:
⇒ 4(1 - cos2θ) = 3(1 + cosθ)
⇒ 4(1 - cosθ)(1 + cosθ) = 3(1 + cosθ)
⇒ 4(1 - cosθ) = 3
⇒ 4 - 4cosθ = 3
⇒ cosθ = 1 /4
⇒ secθ = 4
⇒ sinθ = √ 15 / 4
⇒ tanθ = √ 15
\(\rm √{15}\tan \theta+\frac{4}{√{15}}\sin \theta+2\sec \theta\)
⇒ √15 × √15 + 4 / √15 × √15 / 4 + 2 × 4
⇒ 15 + 1 + 8
⇒ 24
∴ The correct answer is 24.
Last updated on Jun 17, 2025
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