MCQ
If $A$ and $B$ are acute angles such that $\sin\text{A}=\cos\text{B}$ then $(\text{A}+\text{B})=?$
- A$45^\circ$
- B$60^\circ$
- ✓$90^\circ$
- D$180^\circ$
✓
Answer
Correct option: C.
$90^\circ$
$\sin\text{A}=\cos\text{B}$
$\Rightarrow\sin\text{A}=\sin(90^\circ-\text{B})$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\text{A}+\text{B}=90^\circ$
$\Rightarrow\sin\text{A}=\sin(90^\circ-\text{B})$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\text{A}+\text{B}=90^\circ$
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