Question

How do you use sum to product formulas to write the sum or difference `sin60^circ+sin90^circ` as a product?

Answer 1

`sin60^@+sin90^@=2sin75^@cos15^@`

Explanation:

As the sum to product formula for sum of two sines is

`sinX+sinY=2sin((X+Y)/2)cos((X-Y)/2)`

Hence `sin60^@+sin90^@`

= `sin90^@+sin60^@`

= `2sin((90^@+60^@)/2)cos((90^@-60^@)/2)`

= `2sin75^@cos15^@`