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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
$\cos \left(\tan ^{-1} x\right)=$
  • A
    $\sqrt{1+x^2}$
  • ✓
    $\frac{1}{\sqrt{1+x^2}}$
  • C
    $1+x^2$
  • D
    $\frac{1}{1+x^2}$
✓

Answer

Correct option: B.
$\frac{1}{\sqrt{1+x^2}}$
(B) $\cos \left(\tan ^{-1} x\right)=\cos \left[\cos ^{-1} \frac{1}{\sqrt{1+x^2}}\right]$ $\ldots\left[\because \tan ^{-1} x=\cos ^{-1}\left(\frac{1}{\sqrt{1+x^2}}\right)\right]$
$=\frac{1}{\sqrt{1+x^2}}$

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