Question

Please help me solve that question​

Answer 1

Step-by-step explanation:

$\sin(\theta + \phi) = 2\cos(\theta - \phi)$

Using the addition identity formulas, we can write

$\sin{\theta}\cos{\phi} + \cos{\theta}\sin{\phi} = 2\cos{\theta}\cos{\phi} + 2\sin{\theta}\sin{\phi}$

Dividing both sides by $\cos{\phi}$, we get

$\sin{\theta} + \cos{\theta}\tan{\phi} = 2\cos{\theta} + 2\sin{\theta}\tan{\phi}$

Dividing both sides by $\sin{\theta}$, we get

$\tan{\theta} + \tan{\phi} = 2 + 2\tan{\theta}\tan{\phi}$

or

$\tan{\theta}(1 - 2\tan{\phi}) = 2 - \tan{\phi}$

Rearranging the terms,

$\tan{\theta} = \dfrac{2 - \tan{\phi}}{1 - 2\tan{\phi}}$