MCQ
$\sin [{\cot ^{ - 1}}(\cos {\tan ^{ - 1}}x)] =$
- A$\frac{x}{{\sqrt {{x^2} + 2} }}$
- B$\frac{x}{{\sqrt {{x^2} + 1} }}$
- C$\frac{1}{{\sqrt {{x^2} + 2} }}$
- ✓$\sqrt {\frac{{{x^2} + 1}}{{{x^2} + 2}}} $
✓
Answer
Correct option: D.
$\sqrt {\frac{{{x^2} + 1}}{{{x^2} + 2}}} $
d
(d) $\sin \,[{\cot ^{ - 1}}\,(\cos \,\,{\tan ^{ - 1}}x)]$
(d) $\sin \,[{\cot ^{ - 1}}\,(\cos \,\,{\tan ^{ - 1}}x)]$
$ = \sin \,\left[ {{{\cot }^{ - 1}}\,\left( {\cos \,\,{{\cos }^{ - 1}}\frac{1}{{\sqrt {1 + {x^2}} }}} \right)} \right]$
$ = \sin \,\left[ {{{\cot }^{ - 1}}\frac{1}{{\sqrt {1 + {x^2}} }}} \right] = \sin \,\left[ {{{\sin }^{ - 1}}\sqrt {\frac{{1 + {x^2}}}{{2 + {x^2}}}} } \right]$
$ = \sqrt {\frac{{1 + {x^2}}}{{2 + {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.
Explore more
Similar questions
$\left| {\,\begin{array}{*{20}{c}}{11}&{12}&{13}\\{12}&{13}&{14}\\{13}&{14}&{15}\end{array}\,} \right| = $
→${\cos ^{ - 1}}\frac{4}{5} + {\tan ^{ - 1}}\frac{3}{5} = $
→A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement, then the probability that exactly two of the three balls were red, the first ball being red, is
→- $\frac{1}{3}$
- $\frac{4}{7}$
- $\frac{15}{28}$
- $\frac{5}{28}$
If a line makes angles $\alpha ,\beta ,\gamma ,\delta $ with four diagonals of a cube, then the value of ${\sin ^2}\alpha + {\sin ^2}\beta + $ ${\sin ^2}\gamma + {\sin ^2}\delta $ is
→Area between the curves $y = x^3$ and $y = \sqrt x$ is
→The number of real solution of the equation
$\sqrt{1+\cos2\text{x}}=\sqrt2\sin^{-1}(\sin\text{x}),-\pi\leq\text{x}\leq\pi$ is:
→$\sqrt{1+\cos2\text{x}}=\sqrt2\sin^{-1}(\sin\text{x}),-\pi\leq\text{x}\leq\pi$ is:
- 0
- 1
- 2
- infinite
The values of $x$, at which the first derivative of the function ${\left( {\sqrt x + {1 \over {\sqrt x }}} \right)^2}$ w.r.t. $x$ is ${3 \over 4}$, are
→Feasible region (shaded) for a LPP is shown in the given figure. Minimum of z = 4x + 3y occurs at the point.
If $f(x) \, \& \,g(x)$ are inverse functions of each other such that $f(1) = 3\, \& \,f(3) = 1,$ then $\int\limits_1^3 {\left( {g(x) + \frac{x}{{f'\left( {g\left( x \right)} \right)}}} \right)} dx$ is equal to -
→A normal to the plane x = 2 is: