MCQ
If $\sec\text{4A}=\text{cosec}(\text{A}-10^\circ)$ and $\text{4A}$ is acute then $\angle\text{A}=?$
- ✓$20^\circ$
- B$30^\circ$
- C$40^\circ$
- D$50^\circ$
✓
Answer
Correct option: A.
$20^\circ$
$\sec\text{4A}=\text{cosec}(\text{A}-10^\circ)$
$\Rightarrow\text{cosec}(90^\circ-\text{4A})=\text{cosec}(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{4A}=\text{A}-10^\circ$
$\Rightarrow\text{5A}=100^\circ$
$\Rightarrow\text{A}=20^\circ$
$\Rightarrow\text{cosec}(90^\circ-\text{4A})=\text{cosec}(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{4A}=\text{A}-10^\circ$
$\Rightarrow\text{5A}=100^\circ$
$\Rightarrow\text{A}=20^\circ$
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