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

Question : If $\sin A=-\frac{3}{5}, A$ lies in III quadrant, the value of $\sec A$ is:

Option 1: $-\frac{4}{5}$

Option 2: $-\frac{5}{4}$

Option 3: $-\frac{3}{4}$

Option 4: $\frac{3}{4}$

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:

Option 1: 0

Option 2: 1

Option 3: 0.1

Option 4: 0.5

Question : If $\frac{\sin x-\cos x}{\sin x+\cos x}=\frac{2}{5}$, then the value of $\frac{1+\cot ^2 x}{1-\cot ^2 x}$ is:

Option 1: 2.25

Option 2: 1.45

Option 3: 3.75

Option 4: 5.25

Question : If $\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta}=\frac{1}{7}, \theta$ lies in first quadrant, then the value of $\frac{\operatorname{cosec} \theta+\cot ^2 \theta}{\operatorname{cosec} \theta-\cot ^2 \theta}$ is:

Option 1: $\frac{19}{5}$

Option 2: $\frac{22}{3}$

Option 3: $\frac{37}{12}$

Option 4: $\frac{37}{19}$