1 + ^2 ( ^ - 1 x) = - Vidyadip

MCQ

$1 + {\cot ^2}({\sin ^{ - 1}}x) = $

A
$\frac{1}{{2x}}$
B
${x^2}$
✓
$\frac{1}{{{x^2}}}$
D
$\frac{2}{x}$

✓

Answer

Correct option: C.

$\frac{1}{{{x^2}}}$

c
(c) Let ${\sin ^{ - 1}}x = \theta \,\, \Rightarrow \,\,\sin \theta = x$

Now $1 + {\cot ^2}\theta = \cos e{c^2}\theta = \frac{1}{{{x^2}}}$

Hence $1 + {\cot ^2}\,({\sin ^{ - 1}}x) = \frac{1}{{{x^2}}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 2. inverse trigonometric function→STD 12 - 2. inverse trigonometric function — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

A solid hemisphere is attached to the top of a cylinder, having the same radius as that of the cylinder. If the height of the cylinder were doubled (keeping both radii fixed), the volume of the entire system would have increased by $50\,\%$. By what percentage would the volume have increased if the radii of the hemisphere and the cylinder were doubled (keeping the height fixed)?

If the rate of increase of area of a circle is not constant but the rate of increase of $(perimeter)$ is constant, then the rate of increase of area varies

The distance of the point $P (4,6,-2)$ from the line passing through the point $(-3,2,3)$ and parallel to a line with direction ratios $3,3,-1$ is equal to :

Let $R$ be a relation defined on $N$ as a $R$ b is $2 a+3 b$ is a multiple of $5, a, b \in N$. Then $R$ is

Evaluate $\begin{bmatrix}5&0&5\\1&4&3\\0&8&6\end{bmatrix}$ is:

If $a = 2i + j - k,\,\,b = i + 2j + k$ and $c = i - j + 2k,$ then $a\,.\,(b \times c) = $

$\int\text{e}^{\text{x}}\Big(\frac{1-\sin\text{x}}{1-\cos\text{x}}\Big)\text{dx}=$

Two persons $A$ and $B$ take turns in throwing a pair of dice.The first person to throw $9$ from both dice will be awarded the prize. If $A$ throws first, then the probability that $B$ wins the game is.

The derivative of $\sin ^2 x$ w.r.t. $e^{\cos x} i$

An anti-aircraft gun take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shot are $0.4, 0.3, 0.2$ and $0.1$ respectively. The probability that the gun hits the plane is