Question

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

Answer 1

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^@)`