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]

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

Using the complementary angle identity $\cos \theta = \sin (90^\circ - \theta)$, we have:

Substitute this into the expression:

Using the complementary angle identity $\sin \theta = \cos (90^\circ - \theta)$, we have:

Substitute this into the expression:

Substitute the values from Step 1, Step 2, and Step 3 into the original expression:

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