Question

How do you solve `sin(x+(3pi)/4)+sin(x-(3pi)/4)=1`?

Answer 1

`x = pi/4 and x = (3pi)/4`

Explanation:

Use the trig identity:
sin (a + b) + sin (a - b) = 2sin a.cos b
a = x
`b = pi/4`
2sin x.cos (pi)/4 = 1
`2sin x(sqrt2/2) = 1`
`sin x = (1/sqrt2) = sqrt2/2`
Trig table and unit circle give 2 arcs x that have same sine value:
`x = pi/4 and x = (3pi)/4`