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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\cos \left(\sin ^{-1} \frac{5}{13}\right)=$
  • ✓
    $\frac{12}{13}$
  • B
    $-\frac{12}{13}$
  • C
    $\frac{5}{12}$
  • D
    $-\frac{5}{12}$
✓

Answer

Correct option: A.
$\frac{12}{13}$
(A) Let $\sin ^{-1} \frac{5}{13}=x \Rightarrow \sin x=\frac{5}{13}$
$\Rightarrow \cos x=\sqrt{1-\frac{25}{169}}=\frac{12}{13}$
$\Rightarrow \cos \left(\sin ^{-1} \frac{5}{13}\right)=\cos \left(\cos ^{-1} \frac{12}{13}\right)=\frac{12}{13}$

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