Sin2A1 + cos2A Substituting the values of nbsp; sin 2A = 2sin A·cos A and cos 2A = 2cos^2 A 1 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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Trigonometric Ratios of Multiples of an Angle

sin2A/1 + cos...

Question

$\frac{sin 2 A}{1 + cos 2 A}$ =

$tan A$

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$cot A$

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$\frac{2 tan \frac{A}{2}}{1 - {tan}^{2} \frac{A}{2}}$

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$tan 2 A$

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Solution

The correct option is C
$\frac{2 tan \frac{A}{2}}{1 - {tan}^{2} \frac{A}{2}}$

$\frac{sin 2 A}{1 + cos 2 A}$

Substituting the values of $sin 2 A = 2 sin A \cdot cos A$ and $cos 2 A = 2 {cos}^{2} A - 1$

$= \frac{2 sin A . cos A}{1 + 2 {cos}^{2} A - 1}$

$= \frac{2 sin A . cos A}{2 {cos}^{2} A} = tan A$

We know, $tan 2 A = \frac{2 tan A}{1 - {tan}^{2} A}$

So, $tan A = \frac{2 tan \frac{A}{2}}{1 - {tan}^{2} \frac{A}{2}}$

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