Holly G.

# find all solutions to the equation in (0, 2pi) sin(6x)+sin(2x)=0

find all solutions to the equation in (0 to 2pi)

sin(6x)+sin(2x)=0

## 3 Answers By Expert Tutors

By: Math Physics and Chemistry Expert Robert J.

Your trig identity sin(a) + sin(b) = 2sin( (a+b)/2)*sin((a-b)/2)  is incorrect.

Don't memerize the formula. Use reasoning to derive it.

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11/09/12 Certified High School AP Calculus and Physics Teacher Michael B.

Correct, but your (lack of) explanation about why sin(4x+2x)+sin(4x-2x)=2sin(4x)cos(2x) probably isn't clear to the OP.  To clarify for benefit of OP, here's why:

Sum of Sines formula(s):

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Therefore:

sin(a + b) + sin(a - b)
=   sin(a)cos(b) + cos(a)sin(b)
+ sin(a)cos(b) - cos(a)sin(b)
=   2 sin(a) cos(b)

(Notice how cos(a) sin(b) cancels out, and sin(a)cos(b) gets doubled).

Now apply sin(4x + 2x) + sin(4x - 2x), and you'll get Robert's solution.

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11/12/12 