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Trigonometric Ratios Of Compound Angles — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Ratios Of Compound Angles1 Mark
Question
$\frac{\sin3\text{x}}{1+2\cos2\text{x}}$ is equal to:
  1. $\cos\text{x}$
  2. $\sin\text{x}$
  3. $-\cos\text{x}$
  4. $\sin\text{x}$
✓

Answer

  1. $\sin\text{x}$

Solution:

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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