What is the value of 3sin²30° + $$\frac{3}{5}$$cos²60° - 2sec²45°?

Solution (By Examveda Team)

$$\eqalign{ & 3{\sin ^2}{30^ \circ } + \frac{3}{5}{\cos ^2}{60^ \circ } - 2{\sec ^2}{45^ \circ } \cr & = 3 \times \frac{1}{4} + \frac{3}{5} \times \frac{1}{4} - 2 \times 2 \cr & = \frac{3}{4} + \frac{1}{5} \times \frac{3}{4} - 4 \cr & = \frac{3}{4} + \frac{3}{{20}} - 4 \cr & = \frac{{15 + 3 - 80}}{{20}} \cr & = \frac{{ - 62}}{{10}} \cr & = \frac{{ - 31}}{{10}} \cr} $$