MCQ
$\int_{}^{} {\frac{{\cot x}}{{\log \sin x}}} \;dx = $
  • $\log (\log \sin x) + c$
  • B
    $\log (\log {\rm{cosec}}\,x) + c$
  • C
    $2\log (\log \sin x) + c$
  • D
    None of these

Answer

Correct option: A.
$\log (\log \sin x) + c$
a
(a)Put $\log \sin x = t$.

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

Similar questions

Area enclosed by the circle $x^2+y^2=a^2$ is equal to:
If $A\,(1\,,\,\,2,\,\, - 1)$ and $B( - 1,\,\,0,\,\,1)$ are given, then the co-ordinates of $P $ which divides $AB$ externally in the ratio $1:2$, are
Let $F(\alpha ) = \left[ {\begin{array}{*{20}{c}}{\cos \alpha }&{ - \sin \alpha }&0\\{\sin \alpha }&{\cos \alpha }&0\\0&0&1\end{array}} \right]$, where $\alpha \in R.$ Then ${[F(\alpha )]^{ - 1}}$ is equal to
If $\text{A} = \displaystyle \left[ \begin{matrix} 1 &\text{amp ; 2} \\ 3&\text{amp; 4} \end{matrix} \right],$ then number of elements in $A$ are :
Let $M$ and $N$ be two $3 \times 3$ non-singular skew-symmetric matrices such that $M N=N M$. If $P^T$ denotes the transpose of $P$, then $M^2 N^2\left(M^T N\right)^{-1}\left(M N^{-1}\right)^T$ is equal to

$(A)$ $M^2$ $(B)$ $-N^2$ $(C)$ $-M^2$ $(D)$ $M N$

Area of the region $\left\{(x, y): x^2+(y-2)^2 \leq 4\right.$, $\left.x^2 \geq 2 y\right\}$ is
If $f (x + y) = f (x) + f (y) + | x | y + xy^2$, $\forall x, y \in R$ and $f ‘ (0) = 0$, then
The eqution of the plane which cute equal intercepts of unit length on the coordinate axes is:
Let $\hat{u}=u_1 \hat{i}+u_2 \hat{j}+u_3 \hat{k}$ be a unit vector in $\mathbb{R}^3$ and $\hat{v}=\frac{1}{\sqrt{6}}(\hat{i}+\hat{j}+2 \hat{k})$. Given that there exists is(are) correct?

($A$) There is exactly one choice for such $\vec{v}$

($B$) There are infinitely many choices for such $\vec{v}$

($C$) If $\hat{u}$ lies in the $x y$-plane then $\left|u_1\right|=\left|u_2\right|$

($D$) If $\hat{u}$ lies in the $x z$-plane then $2\left|u_1\right|=\left|u_3\right|$

Let ${\Delta _1} = \left| {\,\begin{array}{*{20}{c}}{{a_1}}&{{b_1}}&{{c_1}}\\{{a_2}}&{{b_2}}&{{c_2}}\\{{a_3}}&{{b_3}}&{{c_3}}\end{array}\,} \right|$ and ${\Delta _2} = \left| {\,\begin{array}{*{20}{c}}{{\alpha _1}}&{{\beta _1}}&{{\gamma _1}}\\{{\alpha _2}}&{{\beta _2}}&{{\gamma _2}}\\{{\alpha _3}}&{{\beta _3}}&{{\gamma _3}}\end{array}\,} \right|$, then ${\Delta _1} \times {\Delta _2}$ can be expressed as the sum of how many determinants