How do you use the sum to product formulas to write the sum or difference #sin60^circ+sin30^circ# as a product?

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Answer 1 · 2017-03-15T18:37:02

see below

Use the formula
#color(red)(sinx+siny=2 sin (1/2) (x+y)* cos (1/2) ( x-y)#

Therefore,

#sin 60^@+sin30^@=2sin(1/2)(60^@+30^@)*cos(1/2)(60^@-30^@)#

#=2 sin (90^@/2)*cos(30^@/2)#

#=2 sin 45^@ cos 15^@#

#:. color(blue)(sin 60^@+sin30^@=2 sin 45^@ cos 15^@)#