3x 1+2 2x is equal to: 1. 2. 3. - 4. - Vidyadip

Question

$\frac{\sin3\text{x}}{1+2\cos2\text{x}}$ is equal to:

$\cos\text{x}$
$\sin\text{x}$
$-\cos\text{x}$
$\sin\text{x}$

✓

Answer

$\sin\text{x}$

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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