Question : If $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, find the value of $(\cos \theta-\operatorname{sin} \theta)$

Option 1: $\sqrt{2} \sin \theta$

Option 2: $\sqrt{2} \cos \theta$

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

Option 4: $\frac{1}{2}\cos \theta$

Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:

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

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

Option 3: $\frac{5}{2 \sqrt{3}}$

Option 4: $\frac{5}{3 \sqrt{3}}$

Question : If $\sin (A-B)=\sin A \cos B–\cos A\sin B$, then $\sin 15°$ will be:

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

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

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

Option 4: $\frac{\sqrt{3}–1}{2\sqrt{2}}$

Question : If $\sin A=\frac{2}{3}$, then find the value of (7 – tan A)(3 + cos A).

Option 1: $\frac{61}{3}+\frac{17}{3 \sqrt{5}}$

Option 2: $\frac{61}{3 \sqrt{5}}+\frac{17}{3}$

Option 3: $\frac{61}{3}+\frac{17}{\sqrt{5}}$

Option 4: $\frac{61}{3}-\frac{17}{3 \sqrt{5}}$

Question : If $4-2 \sin ^2 \theta-5 \cos \theta=0,0^{\circ}<\theta<90^{\circ}$, then the value of $\cos \theta-\tan \theta$ is:

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

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

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

Option 4: $\frac{1-2 \sqrt{3}}{2}$