Question

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

Answer 1

꧁Answer࿐

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