Question : The value of tan 25° tan 35° tan 45° tan 55° tan 65° is:
Option 1: $2$
Option 2: $1$
Option 3: $\sqrt{3}$
Option 4: $0$
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Correct Answer: $1$
Solution : The trigonometric identity $\tan A.\cot A = 1$ and $\tan (90° -\theta) = \cot \theta$ $\tan 25° \tan 35° \tan 45° \tan 55° \tan 65°$ $ = \tan 25°×\tan 35° \times 1\times \tan(90° - 35°)×\tan(90° - 25°)$ $ = \tan 25° ×\tan 35° \times 1\times \cot 35°× \cot 25°$ $ = 1$ Hence, the correct answer is 1.
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Question : What is the value of $\sin 28° \sin 35° \sin 45° \sec 62° \sec 55°$?
Option 2: $\frac{1}{\sqrt{2}}$
Option 3: $\sqrt{2}$
Option 4: $\frac{1}2$
Question : Using $\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \tan B}$, find the value of $\tan 15°$.
Option 1: $\sqrt{3}+1$
Option 2: $\sqrt{3}-1$
Option 3: $2-\sqrt{3}$
Option 4: $2+\sqrt{3}$
Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?
Option 1: $\sqrt{3}$
Option 3: $\frac{1}{\sqrt{3}}$
Option 4: ${\sqrt{2}}$
Question : The value of $\tan 5^{\circ} \tan 25^{\circ} \tan 45^{\circ} \tan 65^{\circ} \tan 85^{\circ}$ is ______.
Option 1: 4
Option 2: 3
Option 3: 1
Option 4: 2
Question : If $\tan (A+B)=\sqrt{3}$ and $\tan (A-B)=\frac{1}{\sqrt{3}}; 0°<(A+B)<90°; A > B$, then the values of $A$ and $B$ are respectively:
Option 1: 45° and 15°
Option 2: 15° and 45°
Option 3: 30° and 30°
Option 4: 60° and 30°
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