Question

Evaluate the following expressions :
$2si{n}^2{30}^{\circ }tan{60}^{\circ }-3co{s}^2{60}^{\circ }se{c}^2{30}^{\circ }$

Answer 1

We have,
$2si{n}^2{30}^{\circ }tan{60}^{\circ }-3co{s}^2{60}^{\circ }{60}^{\circ }se{c}^2{30}^{\circ }$
$=2(sin{30}^{\circ }{)}^{2}tan{60}^{\circ }-3(cos{60}^{\circ }{)}^2(sec{30}^{\circ }{)}^2$
$=2\times {\left(\frac{1}{2}\right)}^2\times \sqrt{3}-3\times \frac{1}{4}\times \frac{4}{3}=\frac{\sqrt{3}}{2}-1=\frac{\sqrt{3}-2}{2}$