Question

If tan theta =2,then find the value of 2sin theta cos theta/cos^2 theta-sin^2 theta​

Answer 1

Answer:

$- \frac{4}{3}$

Step-by-step explanation:

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Answer 2

$\red{ \bold{ \underline{ \bf{ANSWER }}}} \\ \rightarrow \: \frac{ \: 4}{ - 3}$

$\green{formula \: used}$

$\rightarrow \sin(2 \varnothing) = 2 \sin(\varnothing) \cos(\varnothing) \\ \rightarrow \cos(2\varnothing) = { \cos(\varnothing) }^{2} - { \sin(\varnothing) }^{2} \\ \rightarrow \tan(2\varnothing) = \frac{2 \tan(\varnothing) }{1 - { \tan(\varnothing) }^{2} } \\ \rightarrow \tan(\varnothing) = \frac{ \sin(\varnothing) }{ \cos(\varnothing) }$

$\\ \green{solution}$

$\rightarrow \frac{2\sin(\varnothing) \cos(\varnothing) }{{ \cos(\varnothing) }^{2} - { \sin(\varnothing) }^{2}} = \frac{ \sin(2 \varnothing)}{ \cos(2\varnothing)} = \tan(2\varnothing)$

$\rightarrow\tan(2\varnothing) = \frac{2 \tan(\varnothing) }{1 - { \tan(\varnothing) }^{2} } \\ \\ \text{since \: tan(theta ) = 2} \\ \\ \rightarrow\tan(2\varnothing) = \frac{2 \times 2}{1 - {2}^{2} } = \frac{ \: 4}{ - 3}$