Download App

2. inverse trigonometric function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
${\tan ^{ - 1}}\frac{{1 - {x^2}}}{{2x}} + {\cos ^{ - 1}}\frac{{1 - {x^2}}}{{1 + {x^2}}} = $
  • A
    $\frac{\pi }{4}$
  • ✓
    $\frac{\pi }{2}$
  • C
    $\pi $
✓

Answer

Correct option: B.
$\frac{\pi }{2}$
b
(b) Putting $x = \tan \theta $

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

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

$ = {\tan ^{ - 1}}(\cot 2\theta ) + {\cos ^{ - 1}}(\cos 2\theta )$

$ = \frac{\pi }{2} - 2\theta + 2\theta = \frac{\pi }{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

Find the determinant of the matrix $\text{A}=\begin{bmatrix}-\cos\theta&-tan\theta\\\cot\theta&\cos\theta\end{bmatrix}$ is:
  1. $\sin^2\theta$
  2. $\sin\theta$
  3. $-\sin\theta$
  4. $-\sin^2\theta$
→
$\int\limits^\infty_0\frac{1}{1+\text{e}^\text{x}}\text{dx}$ equals:

  1. $\log2-1$

  2. $\log2$

  3. $\log4-1$

  4. $-\log2$

→
A matrix consisting of a single column of m elements is know as:
  1. Column matrix
  2. Row matrix
  3. Square matrix
  4. Null matrix
→
The function $f(x) = x(x + 3){e^{ - (1/2)x}}$ satisfies all the conditions of Rolle's theorem in $ [-3, 0]$. The value of $c$ is
→
If $\text{x}=\text{f}(\text{t})\cos\text{t}-\text{f}(\text{t})\sin\text{t}\ \text{and}\ \text{y}=\text{f}(\text{t})\sin\text{t}+\text{f}(\text{t})\cos\text{t},$ then $\Big(\frac{\text{dx}}{\text{dt}}\Big)^2+\Big(\frac{\text{dy}}{\text{dt}}\Big)^2=$
  1. $\text{f}(\text{t})-\text{f}(\text{t})$
  2. $\{\text{f}(\text{t})-\text{f}(\text{t})\}^2$
  3. $\{\text{f}(\text{t})+\text{f}(\text{t})\}^2$
  4. $\text{None of these}$
→
If $\left| \begin{array}{*{20}{c}}
{ - 2a}&{a + b}&{a + c}\\
{b + a}&{ - 2b}&{b + c}\\
{c + a}&{b + c}&{ - 2c}
\end{array}\right|$ $ = \alpha \left( {a + b} \right)\left( {b + c} \right)\left( {c + a} \right) \ne 0$ then $\alpha $ is equal to
→
Choose the correct answer from the given four options:
The area of the region bounded by the ellipse $\frac{\text{x}^2}{25}+\frac{\text{y}^2}{16}=1$ is:
  1. $20\pi\text{ sq. units}$
  2. $20\pi^2\text{ sq. units}$
  3. $16\pi^2\text{ sq. units}$
  4. $25\pi\text{ sq. units}$
→
The projection of vectors $\vec{a}=2 \dot{i}-\hat{j}+\vec{k}$ on the vector $\vec{b}=\dot{i}+2 \dot{j}+2 \dot{k}$ is _________ .
→
Which of the following statements is false?
→
The determinant $\left| {\,\begin{array}{*{20}{c}}a&b&{a\alpha + b}\\b&c&{b\alpha + c}\\{a\alpha + b}&{b\alpha + c}&0\end{array}\,} \right| = 0$, if $a,b,c$ are in
→