trigonometry
posted by george .
14. Solve sin 2x + sin x = 0 for 0 ≤ x ≤ 2π.
21. Write 2sin37°sin26° as a sum (or difference).

14.
sin 2x + sinx = 0
2sinxcosx + sinx = 0
sinx(2cosx + 1) = 0
sinx = 0 or sinx = 1/2
for sinx = 0
x = 0, π, 2π
for sinx = 1/2
x = 7π/6 or 11π/6 ( 210° or 330°)
21.
recall:
cos u  cosv = 2sin( (u+v)/2 ) sin( (uv)/2 )
let (u+v)/2 = 37 > u+v = 74
let (uv)/2= 26 > uv = 52
add them:
2u = 126
u = 63 , then v = 11
2 sin((63+11)/2) sin((6311)/2) = cos 63  cos 11
2 sin((63+11)/2) sin((6311)/2) = cos11°  cos63°