Answer
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ + $\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.99999998
or
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ + $\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 1
Work Step by Step
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ + $\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$
Evaluate each piece:
$\sin$ 35$^{\circ}$ $\approx$ 0.57357643
$\cos$ 55$^{\circ}$ $\approx$ 0.57357643
$\cos$ 35$^{\circ}$ $\approx$ 0.81915204
$\sin$ 55$^{\circ}$ $\approx$ 0.81915204
Combine:
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ $\approx$ 0.32898992
$\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.67101006
0.32898992 + 0.67101006 $\approx$ 0.99999998
Therefore:
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ + $\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 0.99999998
or
$\sin$ 35$^{\circ}$$\cos$ 55$^{\circ}$ + $\cos$ 35$^{\circ}$$\sin$ 55$^{\circ}$ $\approx$ 1
