The value of sin²30°.cos²45° + 2tan²30° - sec²60° is equal to:

Solution (By Examveda Team)

$$\eqalign{ & {\sin ^2}{30^ \circ }.{\cos ^2}{45^ \circ } + 2{\tan ^2}{30^ \circ } - {\sec ^2}{60^ \circ } \cr & = {\left( {\frac{1}{2}} \right)^2}.{\left( {\frac{1}{{\sqrt 2 }}} \right)^2} + 2{\left( {\frac{1}{{\sqrt 3 }}} \right)^2} - {\left( 2 \right)^2} \cr & = \frac{1}{4} \times \frac{1}{2} + 2{\left( {\frac{1}{{\sqrt 3 }}} \right)^2} - {\left( 2 \right)^2} \cr & = \frac{1}{8} + \frac{2}{3} - 4 \cr & = \frac{{3 + 16 - 96}}{{24}} \cr & = - \frac{{77}}{{24}} \cr} $$