(i) sin (75°) = sin (30° + 45°) = sin 30° cos 45° + cos 30° sin 45° [Since sin (A + B) = sin A cos B + cos A sin B] = $\frac{1}{2} \times \frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2} \times \frac{1}{\sqrt{2}}$ = $\frac{1}{2\sqrt{2}} + \frac{\sqrt{3}}{2\sqrt{2}}$ = $\frac{1+\sqrt{3}}{2\sqrt{2}}$ (ii) tan 15° = tan (45° – 30°) = $\frac{\tan 45^{\circ} - \tan 30^{\circ}}{1 + \tan 45^{\circ} \tan 30^{\circ}}$ = $\frac{1 - \frac{1}{\sqrt{3}}}{1 + 1 \times \frac{1}{\sqrt{3}}}$ = $\frac{\sqrt{3} - 1}{\sqrt{3} + 1}$ = 2 - $\sqrt{3}$