Question

Please help me solve that question​

Answer 1

Explanation:

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

Using the addition identity formulas, we can write

`sin(\theta)cos(\phi) + cos(\theta)sin(\phi) = 2cos(\theta)cos(\phi) + 2sin(\theta)sin(\phi)`

Dividing both sides by
`cos(\phi)`, we get

`sin(\theta) + cos(\theta)tan(\phi) = 2cos(\theta) + 2sin(\theta)tan(\phi)`

Dividing both sides by
`sin(\theta)`, we get

`tan(\theta) + tan(\phi) = 2 + 2tan(\theta)tan(\phi)`

or

`tan(\theta)(1 - 2tan(\phi)) = 2 - tan(\phi)`

Rearranging the terms,

`tan(\theta) = (2 - tan(\phi))/(1 - 2tan(\phi))`