Question : The expression $\frac{\tan57°+\cot37°}{\tan33°+\cot53°}$ is equal to:

Option 1: $\tan33°\cot57°$

Option 2: $\tan57°\cot37°$

Option 3: $\tan33°\cot53°$

Option 4: $\tan53°\cot37°$

Question : In $\triangle$ABC, if the median AD = $\frac{1}{2}$BC, then $\angle$BAC is equal to:

Option 1: 90°

Option 2: 45°

Option 3: 60°

Option 4: 75°

Question : What is the value of $\cos45° \sin15°$?

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

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

Option 3: $(\sqrt{3}+1)$

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

Question : If $\tan(\alpha -\beta)=1,\sec(\alpha +\beta)=\frac{2}{\sqrt{3}}$ and $\alpha ,\beta$ are positive, then the smallest value of $\alpha$ is:

Option 1: $142\frac{1}{2}°$

Option 2: $187\frac{1}{2}°$

Option 3: $7\frac{1}{2}°$

Option 4: $37\frac{1}{2}°$

Question : What is the value of $\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$?

Option 1: $2$

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

Option 3: $\sqrt{2}$

Option 4: $\frac{1}2$

Question : The value of $\cot41°.\cot42°.\cot43°.\cot44°.\cot45°.\cot46°.\cot47°.\cot48°.\cot49°$ is:

Option 1: $1$

Option 2: $0$

Option 3: $\frac{\sqrt3}{2}$

Option 4: $\frac{1}{\sqrt2}$