Question : What is $\sin \alpha - \sin\beta$?

Option 1: $2 \cos \frac{\alpha+\beta}{2} \sin \frac{\alpha-\beta}{2}$

Option 2: $2 \sin \frac{\alpha+\beta}{2} \sin \frac{\alpha-\beta}{2}$

Option 3: $2 \cos \frac{\alpha-\beta}{2} \sin \frac{\alpha+\beta}{2}$

Option 4: $2 \cos \frac{\alpha+\beta}{2} \cos \frac{\alpha-\beta}{2}$

Question : If $\frac{\cos \alpha}{\sin \beta} = 10$ and $\frac{\cos \alpha}{\cos \beta} = 11$, the value of $\cos ^2 \beta$ is:

Option 1: $\frac{121}{132}$

Option 2: $\frac{100}{221}$

Option 3: $\frac{88}{108}$

Option 4: $\frac{221}{121}$

Question : If $\alpha +\beta =90^\circ$ and $\alpha :\beta =2:1,$ then the ratio of $\cos \alpha$ to $\cos \beta$ is:

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

Option 2: $1:3$

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

Option 4: $1:2$

Question : If $\frac{\cos\alpha}{\cos\beta}= m$ and $\frac{\cos\alpha}{\sin\beta}= n$, then the value of $(m^{2}+n^{2})\cos^{2}\beta$ is:

Option 1: n²

Option 2: m²

Option 3: mn

Option 4: 1

Question : If $\frac{\cos \beta}{\sec \alpha}=15$ and $\frac{\sin \beta}{\sec \alpha}=16$, the value of $\sin ^2 \beta$ is:

Option 1: $\frac{256}{481}$

Option 2: $-\frac{256}{481}$

Option 3: $\frac{481}{256}$

Option 4: $-\frac{481}{256}$