MHT CET · Maths · Trigonometric Ratios & Identities
If A and B are two angles such that A, B, \(\in(0, \pi)\) and they are not supplementary
angles such that \(\sin A-\sin B=0\), then
- A \(A-B=\frac{\pi}{3}\)
- B \(A-B=\frac{\pi}{2}\)
- C \(A=B\)
- D \(A \neq B\)
Answer & Solution
Correct Answer
(C) \(A=B\)
Step-by-step Solution
Detailed explanation
(D)
\(\sin A-\sin B=0\)
\(\sin A=\sin B\) and we know that \(\sin A=\sin (\pi-A)=\sin B\)
\(\therefore \mathrm{A}=\mathrm{B}\) or \(\pi-\mathrm{A}=\mathrm{B}\)
\(\therefore \mathrm{A}=\mathrm{B}\) or \(\mathrm{A}+\mathrm{B}=\pi\)
Since the angles are not supplementary we say \(\mathrm{A}=\mathrm{B}\).
\(\sin A-\sin B=0\)
\(\sin A=\sin B\) and we know that \(\sin A=\sin (\pi-A)=\sin B\)
\(\therefore \mathrm{A}=\mathrm{B}\) or \(\pi-\mathrm{A}=\mathrm{B}\)
\(\therefore \mathrm{A}=\mathrm{B}\) or \(\mathrm{A}+\mathrm{B}=\pi\)
Since the angles are not supplementary we say \(\mathrm{A}=\mathrm{B}\).
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