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Question: Answered & Verified by Expert
If $\sin (120-A)=\sin (120-B)$ and $0 < A, B < \pi$ then all values of $A$ and $B$ are given by
MathematicsTrigonometric Ratios & IdentitiesCOMEDKCOMEDK 2014
Options:
  • A $A+B=\frac{\pi}{3}$
  • B $A=B$ or $A+B=\frac{\pi}{3}$
  • C $A=B$
  • D $A+B=0$
Solution:
1128 Upvotes Verified Answer
The correct answer is: $A=B$ or $A+B=\frac{\pi}{3}$
Given, equation is
$$
\sin (120-A)=\sin (120-B)
$$
Since, sine is positive in II quadrant.
$\therefore$ Either $120-A=120-B$
$\Rightarrow \quad A=B$
or $\quad 120-A=180-(120-B)$
$\Rightarrow \quad 120-A=60+B \Rightarrow A+B=\frac{\pi}{3}$

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