Question : Using trigonometric formulas, find the value of $(\frac{\sin (x - y)}{\sin (x + y)}) (\frac{\tan x + \tan y}{\tan x - \tan y})$
Option 1: –2
Option 2: 2
Option 3: 0
Option 4: 1

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Question : If $\tan x = \frac{7}{5}$ , the value of $\frac{9 \sin x - \frac{42}{5} \cos x}{15 \sin x + 21 \cos x}$ is:

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Answer 1

Correct Answer: 1

Solution : Given:
$\frac{\sin (x - y)}{\sin (x + y)} (\frac{\tan x + \tan y}{\tan x - \tan y})$
Using $\sin (x + y) = \sin x \cos y + \cos x \sin y$ and $\sin (x - y) = \sin x \cos y - \cos x \sin y$ , we get:
$= (\frac{\sin x \cos y - \cos x \sin y}{\sin x \cos y + \cos x \sin y}) (\frac{\tan x + \tan y}{\tan x - \tan y})$
Dividing both numerator and denominator by $\cos x \cos y$ , we get,
$= (\frac{\frac{\sin x \cos y - \cos x \sin y}{\cos x \cos y}}{\frac{\sin x \cos y + \cos x \sin y}{\cos x \cos y}}) (\frac{\tan x + \tan y}{\tan x - \tan y})$
$= (\frac{\tan x - \tan y}{\tan x + \tan y}) (\frac{\tan x + \tan y}{\tan x - \tan y})$
$= 1$
Hence, the correct answer is 1.

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Question : Using trigonometric formulas, find the value of (sin⁡(x−y)sin⁡(x+y))(tan⁡x+tan⁡ytan⁡x−tan⁡y)Option 1: –2Option 2: 2Option 3: 0Option 4: 1

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Question : Using trigonometric formulas, find the value of $(\frac{\sin (x - y)}{\sin (x + y)}) (\frac{\tan x + \tan y}{\tan x - \tan y})$
Option 1: –2
Option 2: 2
Option 3: 0
Option 4: 1