MCQ
The value of $\sin \cot ^{-1} x$ :
- A$\sqrt{1+x^2}$
- B$x$
- C$\left(1+x^2\right)^{\frac{3}{2}}$
- ✓$\left(1+x^2\right)^{\frac{-1}{2}}$
✓
Answer
Correct option: D.
$\left(1+x^2\right)^{\frac{-1}{2}}$
(D)
$\sin \cot ^{-1} x$
Suppose $\cot ^{-1} x=\theta \therefore x=\cot \theta$
$\therefore \quad \sin \theta=\frac{1}{\sqrt{1+x^2}}$
or $\sin \theta=\left(1+x^2\right)^{\frac{-1}{2}}$ Hence correct option is (D).
$\sin \cot ^{-1} x$
Suppose $\cot ^{-1} x=\theta \therefore x=\cot \theta$
$\therefore \quad \sin \theta=\frac{1}{\sqrt{1+x^2}}$
or $\sin \theta=\left(1+x^2\right)^{\frac{-1}{2}}$ Hence correct option is (D).
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