Question

How do you use the sum to product formulas to write the sum or difference `sin((5pi)/4)-sin((3pi)/4)` as a product?

Answer 1

= 2

Explanation:

Use trig identity:
`sin (a - b) = 2cos ((a + b)/2)sin ((a - b)/2)`
Replace `a` by `(5pi)/4` and `b` by `(3pi)/4` -->
`cos ((a +b)/2) = cos 2pi`, and `sin ((a - b)/2) = sin (pi/2)`
We get:
`sin ((5pi)/4) - sin ((3pi)/4) = 2cos 2pi sin (pi/2) = 2`