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

1 Answer
Mar 15, 2017

see below

Explanation:

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^@)