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Trigonometric Identities — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTrigonometric Identities1 Mark
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.
$20^\circ$
$\sec\text{4A}=\text{cosec}(\text{A}-10^\circ)$
$\Rightarrow\text{cosec}(90^\circ-\text{4A})=\text{cosec}(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{4A}=\text{A}-10^\circ$
$\Rightarrow\text{5A}=100^\circ$
$\Rightarrow\text{A}=20^\circ$

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