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°))