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Trigonometric Identities — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTrigonometric Identities1 Mark
MCQ
If $\sin\text{3A}=\cos(\text{A}-10^\circ)$ and $\text{3A}$ is acute then $\angle\text{A}=?$
  • A
    $35^\circ$
  • ✓
    $25^\circ$
  • C
    $20^\circ$
  • D
    $45^\circ$
✓

Answer

Correct option: B.
$25^\circ$
$\sin\text{3A}=\cos(\text{A}-10^\circ)$
$\Rightarrow\cos(90^\circ-\text{3A})=\cos(\text{A}-10^\circ)$
$\Rightarrow90^\circ-\text{3A}=\text{A}-10^\circ$
$\Rightarrow\text{4A}=100^\circ$
$\Rightarrow\text{A}=25^\circ$

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