Question

(g) (2 sin 60°)(3 kos 60°) + 3 tan 30°​

Answer 1

`(2 \ sin 60)(3\ cos 60) +3\ tan 30\ =\ (5\sqrt3)/(2)`

Explanation:

`(2 \ sin 60)(3 \ cos 60) + 3\ tan 30\\\\= (2 * \frac {\sqrt3}{2}) (3 * (1)/(2))+ (3 * (1)/(\sqrt3))\\\\=(√(3)\ * (3)/(2))+ (3)/(\sqrt3)\\\\=(3\sqrt3)/(2)+(3)/(\sqrt3)\\\\=((3\sqrt3)/(2) * (\sqrt3)/(\sqrt3))+((3)/(\sqrt3) * (2)/(2))\\\\=(3* (\sqrt3)^2)/(2\sqrt3)\ + \ (6)/(2 \sqrt3)\\\\=(3 * 3)/(2 \sqrt3) +(6)/(2 \sqrt3)\\\\=(9+6)/(2\sqrt3)\\\\=(15)/(2\sqrt3) * (\sqrt3)/(\sqrt3)\\\\`

`=(15 \sqrt3)/(2 * (√(3))^2)\\\\=(15 \sqrt 3)/(2 * 3)\\\\=(5\sqrt3)/(2)`