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Let $\sin (\mathrm{A}+\mathrm{B})=1$ and $\sin (\mathrm{A}-\mathrm{B})=\frac{1}{2}$ where $\mathrm{A}, \mathrm{B} \in\left[0, \frac{\pi}{2}\right]$.
What is the value of A?
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What is the value of A?
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Verified Answer
The correct answer is:
$\frac{\pi}{3}$
$\begin{array}{l}\sin (\mathrm{A}+\mathrm{B})=1 \\ \Rightarrow \sin (\mathrm{A}+\mathrm{B})=\sin 90^{\circ} \\ \Rightarrow \mathrm{A}+\mathrm{B}=90^{\circ} \\ & \text { Given } \sin (\mathrm{A}-\mathrm{B})=\frac{1}{2}=\sin 30^{\circ} \\ \Rightarrow \mathrm{A}-\mathrm{B}=30^{\circ}\end{array}$
On solving $(1)$ and $(2)$, we get $\mathrm{A}=60$
$\mathrm{B}=30$
On solving $(1)$ and $(2)$, we get $\mathrm{A}=60$
$\mathrm{B}=30$
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