Evaluate: $2 {\tan }^2 45° + {\cos }^2 30° – {\sin }^2 60°.$
 

As we know,

tan 45° = 1

cos 30° = $\frac{\sqrt{3}}{2}$

sin 60° = $\frac{\sqrt{3}}{2}$ 

Let's, put these values in the given equation:

$=2{\left(1\right)}^2 + {\left(\frac{\surd 3}{2}\right)}^2 – {\left(\frac{\surd 3}{2}\right)}^2$

= 2 + 0

= 2