Question : ABCD is a rectangle of which AC is a diagonal. The value of $(\tan^2\angle CAD+1)\sin^2\angle BAC$ is:

Option 1: $2$

Option 2: $\frac{1}{4}$

Option 3: $1$

Option 4: $0$

Question : The value of $(\frac{1}{\sin\theta}+\frac{1}{\tan\theta})(\frac{1}{\sin\theta}-\frac{1}{\tan\theta})$ is:

Option 1: 0

Option 2: 2

Option 3: 3

Option 4: 1

Question : If $\sec A=\frac{5}{4}$, then the value of $\frac{\tan A}{1+\tan ^2 A}-\frac{\sin A}{\sec A}$ is:

Option 1: 2

Option 2: 1

Option 3: 0

Option 4: 3

Question : If $0°<A<90°$, the value of $\frac{\tan A\ -\ \sec A\ -\ 1}{\tan A\ +\ \sec A\ +\ 1}$ is:

Option 1: $\frac{\sin A-1}{\cos A}$

Option 2: $\frac{1-\sin A}{\cos A}$

Option 3: $\frac{1-\cos A}{\sin A}$

Option 4: $\frac{\sin A+1}{\cos A}$

Question : If $\tan\theta-\cot\theta=0$ and $\theta$ is positive acute angle, then the value of $\frac{\tan(\theta+15)}{\tan(\theta-15)}$ is:

Option 1: $3$

Option 2: $\frac{1}{\sqrt{3}}$

Option 3: $\frac{1}{3}$

Option 4: $\sqrt{3}$

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