Question

Solve:

$2{\tan }^2{45}^{\circ }+{\cos }^2{30}^{\circ }-{\sin }^2{60}^{\circ }+\tan {45}^{\circ }/\cot {45}^{\circ }.$

Answer 1

We have,

$2{\tan }^2{45}^{\circ }+{\cos }^2{30}^{\circ }-{\sin }^2{60}^{\circ }+\tan {45}^{\circ }/\cot {45}^{\circ }$

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

$=2+1=3$

Hence, this is the answer.