If angle a is 45 degrees and angle b is 60 degrees.
find sin(a)cos(b)
½ (sin(105) + sin(345))
½ (sin(105) - sin(345))
½ (sin(345) + cos(105))
½ (sin(345) - cos(105))

  (1/2)(sin(105°) +sin(345°))

Step-by-step explanation:

The relevant identity is ...

  sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))

This falls out directly from the sum and difference formulas for sine.

Here, you have α = 45° and β = 60°, so the relevant expression is ...

  sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))

Recognizing that -15° has the same trig function values that 345° has, this can be written ...

  sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))