Question

Find all the solutions of x,for 0 is less than x is less than 2 pi

a. Sin(x + pi/4 + sin(x - pi/4)= -1

b. Sin(1/3 x+5) = 1/2

Answer 1

recalling that sin pi/4 = cos pi/4 = 1/√2
and
sin(a+b) = sina*cosb + cosa*sinb,

a.
x = 5pi/4 or 7pi/4

b.
x/3+5 = pi/6 or 5pi/6
x = 13pi/2-15