Question : If $\theta$ is an acute angle and $\sin(\theta +18^{\circ} )=\frac{1}{2}$, then the value of $\theta$ in circular measure is:

Option 1: $\frac{\pi}{12}$ radians

Option 2: $\frac{\pi}{15}$ radians

Option 3: $\frac{2\pi}{5}$ radians

Option 4: $\frac{3\pi}{13}$ radians

Question : If $\cos^2 \theta=\frac{3}{4}$, where $\theta$ is an acute angle, then the value of $\sin \left(\theta+30^{\circ}\right)$ is:

Option 1: $1$

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

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

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

Question : If $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$, then the value of $\sin ^4 \theta-\cos ^4 \theta$ is:

Option 1: $\frac{5}{12}$

Option 2: $\frac{12}{13}$

Option 3: $\frac{11}{12}$

Option 4: $\frac{5}{13}$

Question : If $5\cos\theta+12\sin\theta=13,\ 0^0<\theta<90^0$, then the value of $\sin\theta$ is:

Option 1: $\frac{5}{13}$

Option 2: $–\frac{12}{13}$

Option 3: $\frac{6}{13}$

Option 4: $\frac{12}{13}$

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 : If $\theta$ is positive acute angle and $7\cos^{2}\theta+3\sin^{2}\theta =4$, then the value of $\theta$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $45^{\circ}$

Option 4: $90^{\circ}$