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astra-53 [7]
3 years ago
10

Please help me solve that question​

Mathematics
1 answer:
konstantin123 [22]3 years ago
7 0

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}}

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