Question

If tan theta=12/13 find the value of 2sin theta *cos theta /cos^2 - sin^2 theta​

Answer 1

Answer:

$\tan( \alpha ) = \frac{12}{13} = \frac{p}{b} \\ h = \sqrt{ {p}^{2} + {b}^{2} } \\ = \sqrt{144 + 169} \\ = \sqrt{313} \\ to \: find \: \: \: 2 \sin( \alpha ) \times \cos( \alpha ) \: and \: {cos}^{2} \alpha - {sin}^{2} \alpha \\ 2 \sin( \alpha ) \cos( \alpha ) \\ = 2 \times \frac{12}{ \sqrt{313} } \times \frac{13}{ \sqrt{313} } \\ = \frac{312}{313} \\ and \\ {cos}^{2} \alpha - {sin}^{2} \alpha \\ = \frac{144}{313} - \frac{169}{313} \\ = \frac{ - 25}{313}$

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Answer 2

Answer:

Tan theta=sin theta/cos theta

Sin theta =12

Cos theta =13

So,

=2*12*13/13*13-12*12

=312/25