Question

How do you use the sum to product formulas to write the sum or difference `sin(x+pi/2)+sin(x-pi/2)` as a product?

Answer 1

`sin(x+pi/2)+sin(x-pi/2)=0`

Explanation:

We use the formula `sinA+sinB=2sin((A+B)/2)cos((A-B)/2)`

`sin(x+pi/2)+sin(x-pi/2)`

= `2sin(((x+pi/2)+(x-pi/2))/2)cos(((x+pi/2)-(x-pi/2))/2)`

= `2sin((2x)/2)cos(pi/2)`

= `2sinx xx 0`

= `0`