Answer
$\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31' $\approx$ 0
Work Step by Step
$\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31'
Convert minutes to decimals:
$\frac{29}{60}$ = 0.4833
$\frac{31}{60}$ = 0.5166
Therefore:
$\cos$ 75.4833$^{\circ}$ $\cos$ 14.5166$^{\circ}$ - $\sin$ 75.4833$^{\circ}$ $\sin$ 14.5166$^{\circ}$
Utilizing a calculator:
$\cos$ 75.4833$^{\circ}$ $\cos$ 14.5166$^{\circ}$ - $\sin$ 75.4833$^{\circ}$ $\sin$ 14.5166$^{\circ}$
$\approx$ (0.2506)(0.96800) - (0.9680)(0.2506)
$\approx$ 0.2426 - 0.2426
$\approx$ 0
Therefore:
$\cos$ 75$^{\circ}$ 29' $\cos$ 14$^{\circ}$ 31' - $\sin$ 75$^{\circ}$ 29' $\sin$ 14$^{\circ}$ 31' $\approx$ 0
