Write the function in the simplest form: ^ -1 ( 1- x 1+ x ), x< - Vidyadip

MCQ

Write the function in the simplest form: $\tan ^{-1}(\sqrt{\frac{1-\cos x}{1+\cos x}}), x<\pi$

A
$2x$
✓
$\frac{x}{2}$
C
$\frac{\pi}{2}$
D
$\pi$

✓

Answer

Correct option: B.

$\frac{x}{2}$

b
$\tan ^{-1}(\sqrt{\frac{1-\cos x}{1+\cos x}}), x<\pi$

$\tan ^{-1}(\sqrt{\frac{1-\cos x}{1+\cos x}})$

$=\tan ^{-1}(\sqrt{\frac{2 \sin ^{2} \frac{x}{2}}{2 \cos ^{2} \frac{x}{2}}})$

$=\tan ^{-1}\left(\frac{\sin \frac{x}{2}}{\cos \frac{x}{2}}\right)$

$=\tan ^{-1}\left(\tan \frac{x}{2}\right)$

$=\frac{x}{2}$

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

Let $a$ , $b$ and $c$ are real numbers such that $a^2 + b^2 + c^2 = 1$ , then the maximum value of $(4b -3c)^2 + (4a -2c)^2 + (3a -2b)^2$ is

Let the function, $f:[-7,0] \rightarrow R$ be continuous on $[-7,0]$ and differentiable on $(-7,0)$ If $f(-7)=-3$ and $f(x) \leq 2,$ for all $x \in(-7,0),$ then for all such functions $f, f(-1)+f(0)$ lies in the interval

Let $A=\left[\begin{array}{lll}0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right] .$ Then the number of $3 \times 3$ matrices $\mathrm{B}$ with entries from the set $\{1,2,3,4,,5\}$ and satisfying $A B=B A$ is $....$

Choose the correct answer from the given four option. Integrating factor of $\frac{\text{xd}\text{y}}{\text{d}\text{x}}-\text{y}=\text{x}^4-3\text{x}$ is :

Choose the correct answer from the given four options. A box contains $3$ orange balls, $3$ green balls and $2$ blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing $2$ green balls and one blue ball is :

Area of a parallelogram whose adjacent sides are represented by the vectors $2 \hat{i}-3 \hat{k}$ and $4 \hat{j}+2 \hat{k}$ is

The total number of matrices formed with the help of 6 different numbers are:

The distance of the point $(-1, -5, -10)$ from the point of intersection of the line $\vec{\text{r}}.=2\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}+\lambda(3\hat{\text{i}}+4\hat{\text{j}}+12\hat{\text{k}})$ and the plane $\vec{\text{r}}.=(\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}})=5$ is:

Choose the correct answer from the given four options:he two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 - 2 = 0$ intersect at an angle of:

Choose the correct answer The planes : $2x – y + 4z = 5$ and $5x – 2.5y + 10z = 6$ are :