Question

if tan 0 = 12/13 evolute 2sin0cos0 / cos 2 squar 0- sin square 2 0​

Answer 1

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$\frac{2sin \alpha \cos \alpha }{ {cos}^{2} \alpha - {sin \alpha }^{2} } \\ = \frac{sin2 \alpha }{ \cos2 \alpha } \\ = tan2 \alpha \\ = \frac{2tan \alpha }{1 - {tan}^{2} \alpha } \\ = \frac{2( \frac{12}{13} )}{1 - { (\frac{12}{13} )}^{2} } \\ = \frac{ \frac{24}{13} }{ \frac{169 - 144}{169} } \\ = \frac{24}{13} \times \frac{169}{25} \\ = \frac{24 \times 13}{25} \\ = \frac{312}{25} \\ \\ given \: \: tan \alpha = \frac{12}{13} \\ using \: \: tan2 \alpha = \frac{2tan \alpha }{1 - {tan}^{2} \alpha }$