Question

Given sin A = 12/13 A is in Q1, find tan 2A.​

Answer 1

Answer:

The answer is $-\dfrac{120}{119}$

Step-by-step explanation:

Given

    $\sin A=\dfrac{12}{13}$

Therefore

     $\tan 2A=\dfrac{\sin 2A}{\cos 2A}=\dfrac{2\sin A\cos A}{1-2\sin^2A}=\dfrac{2\sin A\sqrt{1-\sin^2A}}{1-2\sin^2A}$

• Using trigonometric identities

                $=\dfrac{2(\frac{12}{13})\sqrt{1-\frac{144}{169}}}{1-2(\frac{144}{169})}\\\\=\dfrac{\frac{24}{13}(\frac{5}{13})}{\frac{169-288}{169}}=\dfrac{120}{-119}=-\dfrac{120}{119}$