Answer
$\cos$$^{2}$ 60$^{\circ}$ + $\sec$$^{2}$ 150$^{\circ}$ - $\csc$$^{2}$ 210$^{\circ}$ = -$\frac{29}{12}$
Work Step by Step
$\cos$$^{2}$ 60$^{\circ}$ + $\sec$$^{2}$ 150$^{\circ}$ - $\csc$$^{2}$ 210$^{\circ}$
$\cos$ 60$^{\circ}$ = $\frac{1}{2}$
$\sec$ 150$^{\circ}$ = -$\frac{2}{\sqrt3}$
$\csc$ 210$^{\circ}$ = $\csc$ 30$^{\circ}$(In Quadrant III) = -2
Therefore:
= ($\frac{1}{2}$)$^{2}$ - (-$\frac{2}{\sqrt3}$)$^{2}$ - (-2)$^{2}$
= $\frac{1}{4}$ + $\frac{4}{3}$ - 4
= $\frac{3+16-48}{12}$
= -$\frac{29}{12}$
$\cos$$^{2}$ 60$^{\circ}$ + $\sec$$^{2}$ 150$^{\circ}$ - $\csc$$^{2}$ 210$^{\circ}$ = -$\frac{29}{12}$
