Question

Evaluate 4sin^3(60)-3cos(30)

Answer 1

Answer:

$4 {sin}^{3} (60)-3\cos(30) \\ =4 \times ( { \frac{ \sqrt{3} }{2} })^{3} - 3 \times ( \frac{ \sqrt{3} }{2} )$

$= 4 \times \frac{9 \sqrt{3} }{8} - \frac{3 \sqrt{3} }{2}$

$= \frac{36 \sqrt{3} }{8} - \frac{3 \sqrt{3} }{2}$

$= \frac{36 \sqrt{3} - 12 \sqrt{3} }{8}$

$= \frac{(36 - 12) \sqrt{3} }{8}$

$= \frac{24 \sqrt{3} }{8}$

$= 3 \sqrt{3}$

$4 {sin}^{3} (60) - 3 \cos(30) = 3 \sqrt{3}$