Question

evaluating 2 tansquare........ following questions please answer it​

Answer 1

We know:

$\quad\quad$• $\mathtt{tan45^{\circ}=1}$

$\quad\quad$• $\mathtt{cos30^{\circ}=\frac{\sqrt{3}}{2}}$

$\quad\quad$• $\mathtt{sin60^{\circ}=\frac{\sqrt{3}}{2}}$

Now, $\mathtt{2\:tan^{2}45^{\circ}+cos^{2}30^{\circ}-sin^{2}60^{\circ}}$

$\mathtt{=2\:(1)^{2}+\big(\frac{\sqrt{3}}{2}\big)^{2}-\big(\frac{\sqrt{3}}{2}\big)^{2}}$

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

$\mathtt{=2}$

This is the required value.