Question

Evaluate $2({\sin }^{2}45+{\cot }^{2}30)-3({\text{cosec}}^{2}60-{\sec }^2{60}^o)$

Answer 1

$2({\sin }^2{45}^o+{\cot }^2{30}^o)-3(cose{c}^2{60}^o-{\sec }^2{60}^o)$

$=2({\left(\frac{1}{\sqrt{2}}\right)}^2+(\sqrt{3}{)}^2)-3({\left(\frac{2}{\sqrt{3}}\right)}^2-(2{)}^2)$

$=2(\frac{1}{2}+3)-3(\frac{4}{3}-4)$

$=2\left(\frac{1+6}{2}\right)-3\cdot \left(\frac{4-12}{3}\right)$

$=7+8$

$=15$.