14.� Solve sin 2x + sin x = 0 for 0 ≤� x �≤ 2�π.

Question

21. Write 2sin37°sin26° as a sum (or difference).

Answer 1

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( (u-v)/2 )

let (u+v)/2 = 37 ---> u+v = 74
let (u-v)/2= 26 ----> u-v = 52
add them:
2u = 126
u = 63 , then v = 11

-2 sin((63+11)/2) sin((63-11)/2) = cos 63 - cos 11
2 sin((63+11)/2) sin((63-11)/2) = cos11° - cos63°