Question

Is sin(α+2π /3) equal to sin(-α+π/3)?
HOW?

Answer 1

Try expanding using:

sin (A+B)=sinA cosB = cosA sinB

Answer 2

sorry, the second = sign should be read as +

Answer 3

I am getting confused with the signs while expanding........ But the terms are equal in both......

Answer 4

what did you get?

Answer 5

SinAcos120+cosAsin120 and - sinAcos120-cosAsin120

Answer 6

LHS is correct. But the RHS should be sin(-A)cos60+cos(-A)sin60

Answer 7

You don't need to expand it. Actually
\[\sin \theta = \sin (180 - \theta)\]
Right ? @bajji

Answer 8

Ya? @ShailKumar

Answer 9

So, put \[ \theta = \alpha + \frac{2\pi}{3}\]

Answer 10

How dos that help the problem.... I did put but the result is sin((540-alpha+2)/3)

Answer 11

Sorry 3alpha.... And if i do the same for the next... It is not equal right?

Answer 12

Actually \[ 180^o = \pi \ rad\]
So \[180^o - (\alpha+2\pi/3) = \pi - (\alpha+2\pi/3) = (-\alpha + \pi /3 )\]

Answer 13

Does this help now ?

Answer 14

Ya..... Great! Both are equal......