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
- A \(A+B=\frac{\pi}{3}\)
- B \(A=B\) or \(A+B=\frac{\pi}{3}\)
- C \(A=B\)
- D \(A+B=0\)
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 \(\quad 120-A=180-(120-B)\) \(\Rightarrow \quad 120-A=60+B \Rightarrow A+B=\frac{\pi}{3}\)
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