Question

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. $A-B=\dfrac{\pi}{3}$
• B. $A-B=\dfrac{\pi}{2}$
• C. $A=B$
• D. $A\ne B$

Hint:

When $\sin A=\sin B$, always check whether angles are equal or supplementary.

Answer 1

The Correct Option is C

Step 1: Simplifying the given equation.
\[ \sin A-\sin B=0 \Rightarrow \sin A=\sin B \]
Step 2: Using sine equality condition.
For $\sin A=\sin B$, either \[ A=B \quad \text{or} \quad A+B=\pi \]
Step 3: Using the given condition.
It is given that $A$ and $B$ are not supplementary, so \[ A+B\ne\pi \]
Step 4: Conclusion.
Hence, the only possible solution is \[ A=B \]