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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
MCQ
$\frac{\sin3\text{x}}{1+2\cos2\text{x}}$ is equal to:
  • A
    $\cos\text{x}$
  • ✓
    $\sin\text{x}$
  • C
    $-\cos\text{x}$
  • D
    $\sin\text{x}$
✓

Answer

Correct option: B.
$\sin\text{x}$
We have,
$\frac{\sin3\text{x}}{1+2\cos2\text{x}}=\frac{3\sin\text{x}-4\sin^2\text{x}}{1+2(1-2\sin^2\text{x})}$
$=\frac{3\sin\text{x}-4\sin^3\text{x}}{1+2-4\sin\text{x}}$
$=\frac{\sin\text{x}(3-4\sin^2\text{x})}{(3-4\sin^2\text{x})}$
$=\sin\text{x}$

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