( ^ - 1 x) = - Vidyadip

MCQ

$\cos ({\tan ^{ - 1}}x) = $

A
$\sqrt {1 + {x^2}} $
✓
$\frac{1}{{\sqrt {1 + {x^2}} }}$
C
$1 + {x^2}$
D
None of these

✓

Answer

Correct option: B.

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

b
(b) Let $\theta = {\tan ^{ - 1}}x\,\, \Rightarrow \,\,x = \tan \theta $

$\therefore \,\,\cos \theta = \frac{1}{{\sqrt {1 + {{\tan }^2}\theta } }} = \frac{1}{{\sqrt {1 + {x^2}} }}$

Hence $\cos \theta = \cos \,({\tan ^{ - 1}}x) = \frac{1}{{\sqrt {1 + {x^2}} }}$.

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 2. inverse trigonometric function→2. inverse trigonometric function — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $f(x+y)=f(x).f(y)$ for all $x, y$ where $ f(0) \ne 0$. If $f(5) = 2$ and $f '(0) = 3,$ then $f '(5)$ is equal to

If $A$ is an idempotent matrix, then $(I + A)^4$ is (where $I$ is identity matrix of order same as $A$ )

Let $\lambda \in R .$ The system of linear equations

$2 x_{1}-4 x_{2}+\lambda x_{3}=1$

$x_{1}-6 x_{2}+x_{3}=2$

$\lambda x_{1}-10 x_{2}+4 x_{3}=3$ is inconsistent for

An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$. Then the relation is

If two events are independent, then.

They must be mutually exclusive.
The sum of their probabilities must be equal to 1.
(a) and (b) both are correct.
None of the above is correctIf two. events are independent, then.

If $f(x)$ satisfies $f(7 -x) = f(7 + x)\ \forall \,x\, \in \,R$ such that $f(x)$ has exactly $5$ real roots which are all distinct such that sum of the real roots is $S$ then $S/7$ is equal to

Let $y=y(x)$ be the solution of the differential equation $(x+y+2)^2 d x=d y, y(0)=-2$. Let the maximum and minimum values of the function $y=y(x)$ in $\left[0, \frac{\pi}{3}\right]$ be $\alpha$ and $\beta$, respectively. If $(3 \alpha+\pi)^2+\beta^2=\gamma+\delta \sqrt{3}, \gamma, \delta \in \mathbb{Z}$, then $\gamma+\delta$ equals....................

Local maximum and local minimum values of the function $(x - 1){(x + 2)^2}$ are

If $\sin \left( {{{\sin }^{ - 1}}\frac{1}{5} + {{\cos }^{ - 1}}x} \right) = 1$, then $x$ is equal to

If $\text{y}=\sin(\text{m}\sin^{-1}\text{x}),$ then $(1-\text{x}^2)\text{y}_2-\text{xy}_1$ is equal to:

m²y
my
-m²y
None of these