Question

What is the value of
3cos² 30+sec²30+3sin 30-tan²60?

Answer 1

$$\begin{gathered} 3{\cos }^{2}30°+{\sec }^{2}30°+3\sin 30°-{\tan }^{2}60° \\ =3\times {\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{2}{\sqrt{3}}\right)}^2+3\times \frac{1}{2}-{\left(\sqrt{3}\right)}^2 \\ =3\times \frac{3}{4}+\frac{4}{3}+\frac{3}{2}-3 \\ =\frac{9}{4}+\frac{4}{3}+\frac{3}{2}-3 \\ =\frac{27+16+18-36}{12} \\ =\frac{25}{12} \end{gathered}$$