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COMEDK · Maths · 8. Trigonometric Ratios & Identities

If \(\sin (120-A)=\sin (120-B)\) and \(0 < A, B < \pi\) then all values of \(A\) and \(B\) are given by

  1. A \(A+B=\frac{\pi}{3}\)
  2. B \(A=B\) or \(A+B=\frac{\pi}{3}\)
  3. C \(A=B\)
  4. D \(A+B=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(A=B\) or \(A+B=\frac{\pi}{3}\)

Step-by-step Solution

Detailed explanation

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 \(\quad 120-A=180-(120-B)\) \(\Rightarrow \quad 120-A=60+B \Rightarrow A+B=\frac{\pi}{3}\)