Download App

Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Write the function in the simplest form: ${\tan ^{ - 1}}\sqrt {\frac{{1 - \cos x}}{{1 + \cos x}}} ,\;0<x < \pi $
✓

Answer

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

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 "2 Marks Questions" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\begin{bmatrix}\text{a }-\text{b}&2\text{a}+\text{c}\\2\text{a}-\text{b}&3\text{c}+\text{d} \end{bmatrix}=\begin{bmatrix}-1&5\\0&13 \end{bmatrix},$ fine the value of b.
→
For what values of $x : \left[\begin{array}{lll}{1} & {2} & {1}\end{array}\right] \left[\begin{array}{lll}{1} & {2} & {0} \\ {2} & {0} & {1} \\ {1} & {0} & {2}\end{array}\right]\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right] = 0.$
→
If $f: R → R$ is defined by $f(x) = x^2 – 3x + 2,$ find $f(f(x)).$
→
Differentiate $\tan^{-1}\Big(\frac{1+\cos\text{x}}{\sin\text{x}}\Big)$ with respect to x.
→
Three digit numbers are formed with the digits 0, 2, 4, 6 and 8. Write the probability of forming a three digit number with the same digits.
→
Verify that the function $x^{2}=2 y^{2} \log y$ (implicit or explicit) is a solution of the differential equation $\left(x^{2}+y^{2}\right) \frac{d y}{d x}-x y=0$
→
The probability of finding a green signal on a busy crossing X is 30%. What is the probability of finding a green signal on X on two consecutive days out of three?
→
If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}},\ \vec{\text{a}}+\vec{\text{b}}-2\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$
→
Evaluate the following integrals:
$\int\log\text{x}\frac{\sin\big\{1+(\log\text{x})^2\big\}}{\text{x}}\text{ dx}$
→
If $\vec{\text{a}}=3\hat{\text{i}}+4\hat{\text{j}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}},$ find the value of $\big|\vec{\text{a}}\times\vec{\text{b}}\big|.$
→