Question
Very-Short and Short-Answer Qustions:
If $\cot\text{A}=\frac43$ and $(\text{A}+\text{B})=90^\circ,$ what is the value of $\sin\text{B}?$
If $\cot\text{A}=\frac43$ and $(\text{A}+\text{B})=90^\circ,$ what is the value of $\sin\text{B}?$
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Answer
Given, $\cot\text{A}=\frac43$$\text{A}+\text{B}=90^\circ$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\cot\text{A}=\cot(90^\circ-\text{B})$
$\Rightarrow\cot\text{A}=\tan\text{B}$
$\Rightarrow\cot\text{A}=\tan\text{B}=\frac43$
$\Rightarrow\text{A}=90^\circ-\text{B}$
$\Rightarrow\cot\text{A}=\cot(90^\circ-\text{B})$
$\Rightarrow\cot\text{A}=\tan\text{B}$
$\Rightarrow\cot\text{A}=\tan\text{B}=\frac43$
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