Without using tables or calculator, evaluate: sin 45 - cos 60 / sin 10 + sin 50 / 2 cos 40 (b) The minute hand of a clock moves from 1:15 to 5:45 in the face of the clock. If the length of the minute hand is 7cm, find correct to three significant figures, the area swept by the minute hand [Take pi = 22/7]

Step 1: Evaluate $\sin 45^\circ$. We know that $\sin 45^\circ = \frac{\sqrt{2}}{2}$.

Step 2: Simplify the term $\frac{\cos 80^\circ}{\sin 10^\circ}$. Using the complementary angle identity $\cos \theta = \sin (90^\circ - \theta)$, we have: $\cos 80^\circ = \sin (90^\circ - 80^\circ) = \sin 10^\circ$ Substitute this into the expression: $\frac{\cos 80^\circ}{\sin 10^\circ} = \frac{\sin 10^\circ}{\sin 10^\circ} = 1$

Step 3: Simplify the term $\frac{\sin 50^\circ}{2 \cos 40^\circ}$. Using the complementary angle identity $\sin \theta = \cos (90^\circ - \theta)$, we have: $\sin 50^\circ = \cos (90^\circ - 50^\circ) = \cos 40^\circ$ Substitute this into the expression: $\frac{\sin 50^\circ}{2 \cos 40^\circ} = \frac{\cos 40^\circ}{2 \cos 40^\circ} = \frac{1}{2}$

Step 4: Combine the simplified terms. Substitute the values from Step 1, Step 2, and Step 3 into the original expression: $\sin 45^\circ - \frac{\cos 80^\circ}{\sin 10^\circ} + \frac{\sin 50^\circ}{2 \cos 40^\circ} = \frac{\sqrt{2}}{2} - 1 + \frac{1}{2}$

Step 5: Perform the arithmetic. $\frac{\sqrt{2}}{2} - 1 + \frac{1}{2} = \frac{\sqrt{2}}{2} - \frac{2}{2} + \frac{1}{2} = \frac{\sqrt{2} - 2 + 1}{2} = \frac{\sqrt{2} - 1}{2}$

The final answer is $\boxed{\frac{\sqrt{2} - 1}{2}}$.