Answer:
(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°))
