Answer
2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$) = $\frac{23}{4}$
Work Step by Step
2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$)
$\tan$ 120$^{\circ}$ = $-\sqrt3$
$\sin$ 150$^{\circ}$ = $\frac{1}{2}$
$\cos$ 180$^{\circ}$ = -1
Therefore:
= 2(-$\sqrt3$)$^{2}$ + 3($\frac{1}{2}$)$^{2}$ -(-1)$^{2}$
= 6 + $\frac{3}{4}$ - 1
= $\frac{24 + 3 -4}{4}$
= $\frac{23}{4}$
2($\tan$$^{2}$ 120$^{\circ}$) + 3($\sin$$^{2}$ 150$^{\circ}$) - ($\cos$$^{2}$ 180$^{\circ}$) = $\frac{23}{4}$
