Please help me solve that question

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asked Feb 3, 2022 212k views

1 Answer

M Afham · Answer 1 · 2022-02-09T00:54:41+0000

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,

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