Question

if tan theta =12/13,show that 2sin theta cos theta/cos² theta-sin² theta =312/25​

Answer 1

Answer:

2 sin theta cos theta divided by cos square theta minus sin square theta> sin 2 theta by cos 2 theta>tan 2 theta>2 tan theta divided by 1 minus tan square theta>2*12/13 divided by 1-144/169>312/25

Answer 2

Answer:

$tan θ= \frac{12}{13}$

$\frac{2sinθcosθ}{cos²θ-sin²θ} \\ = \frac{ \frac{1}{cos²θ}(2sinθcosθ)}{ \frac{1}{cos²θ}(cos²θ-sin²θ)} \\ = \frac{2 \frac{sinθ}{cosθ} }{1 - \frac{sin²θ}{cos²θ} } \\ = \frac{2tanθ}{1-tan²θ} \\ = \frac{2( \frac{12}{13} )}{1 - ( \frac{12}{13})² } \\ = \frac{ \frac{24}{13} }{1- \frac{144}{169} } \\ = \frac{ \frac{24}{13} }{ \frac{169-144}{169} } \\ = \frac{ \frac{24}{13} }{ \frac{25}{169} } \\ = \frac{24}{13} \times \frac{169}{25} \\ = \frac{24}{1} \times \frac{13}{25} \\ = \frac{312}{25}\\mark\:as\: brainlist$