Question

pleeeeeeease someone help me!
find all solutions of the equation in the interval [0,2pi)
sin(x-pi/3)-sin(x+pi/3)=3/2

Answer 1

Use the following:
\[\sin A+\sin B=2\sin(A+B)/2\cos(A-B)/2\]
then solve for sinx.
Try it, if any problem, tell me.

Answer 2

sinA + sin B =2sin(A+B)/2cos(A-B)/2

Answer 3

im sorry i dont really understand, can u explain it a little more?

Answer 4

i would just use the sum and difference formulas again

Answer 5

i think the answer is (7*pi)/6 or 210 degrees.....

Answer 6

It would also be good to use
sin(A-B)-sin(A+B)=-2sinBcosA
A=x
B=pi/3
So sin(x-pi/3)-sin(x+pi/3)=-2sinpi/3cosx=-cosx
-cosx=3/2 cosx=-3/2
cos x cant be less than -1. So i guess the question is wrong

Answer 7

i agree with Mani Jha
question may have a typo or there is no solution

Answer 8

wait i double checked, and i made a mistake somewhere
kunal is right

cos x = -sqrt3/2

x = 5pi/6, 7pi/6

Answer 9

@mani jha, sin(pi/3) = sqrt3/2

Answer 10

oh yeah, sorry for that mistake