Question
$\cot\Big(\text{cosec}^{-1}\frac{5}{3}+\tan^{-1}\frac{2}{3}\Big)=$
  1. $\frac{6}{17}$
  2. $\frac{3}{17}$
  3. $\frac{4}{17}$
  4. $\frac{5}{17}$

Answer

  1. $\frac{6}{17}$

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

If $a, b, c$ be positive real numbers and the value of $\theta = {\tan ^{ - 1}}\sqrt {\frac{{a(a + b + c)}}{{bc}}} + {\tan ^{ - 1}}\sqrt {\frac{{b(a + b + c)}}{{ca}}} + {\tan ^{ - 1}}\sqrt {\frac{{c(a + b + c)}}{{ab}}} $,then $\tan \theta $ is equal to
If f : A → B given by 3f(x) + 2-x = 4 is a bijection, then

  1. $\text{A}=\{\text{x}\in\text{R}:-1<\text{x}<\infty\},$ $\text{B}=\{\text{x}\in\text{R}:2<\text{x}<4\}$

  2. $\text{A}=\{\text{x}\in\text{R}:-3<\text{x}<\infty\},$ $\text{B}=\{\text{x}\in\text{R}:2<\text{x}<4\}$

  3. $\text{A}=\{\text{x}\in\text{R}:-2<\text{x}<\infty\},$ $\text{B}=\{\text{x}\in\text{R}:2<\text{x}<4\}$

  4. $\text{None of these.}$

If $A$ is square matrix such that $A^{2}=A$, then $(1+A)^{3}-7 A$ is equal to
Let $\left| {\begin{array}{*{20}{c}}
  {{{\left( {a - x} \right)}^2}}&{{{\left( {a - y} \right)}^2}}&{{{\left( {a - z} \right)}^2}} \\ 
  {{{\left( {b - x} \right)}^2}}&{{{\left( {b - y} \right)}^2}}&{{{\left( {b - z} \right)}^2}} \\ 
  {{{\left( {c - x} \right)}^2}}&{{{\left( {c - y} \right)}^2}}&{{{\left( {c - z} \right)}^2}} 
\end{array}} \right| = \frac{{ - 351}}{8}$ . If $x, y , z$ are the roots of the equation $8t^3 - 62t^2 + 43t -7 = 0$ and satisfy the determinant above, and $a, b, c$ are distinct number then value of $|(a - b) (b - c) (c - a)|$ is
Suppose $X =\left[x_{i j}\right]$ a matrix, where
$
X=\left[\begin{array}{ccc}
1 & -1 & 2 \\
3 & 4 & -5 \\
2 & -1 & 3
\end{array}\right]
$
Then matrix $Y =\left[m_{i j}\right]$, where $m_{i j}=$ minor of $x_{i j}$ :
The value of $\int_{\,0}^{\,8} {\,|x - 5|\,dx} $ is
Choose the correct answer from the given four options.
Suppose a random variable X follows the binomial distribution with parameters n and p, where 0 < p < 1. If $\frac{\text{P}(\text{x}=\text{r})}{\text{P}(\text{x}=\text{n}–\text{r})}$ is independent of n and r, then p equals:
  1. $\frac{1}{2}$
  2. $\frac{1}{3}$
  3. $\frac{1}{5}$
  4. $\frac{1}{7}$
The value of the determinant $\left| {\,\begin{array}{*{20}{c}}{31}&{37}&{92}\\{31}&{58}&{71}\\{31}&{105}&{24}\end{array}\,} \right|$ is
The probability that a randomly selected $2$ digit number belongs to the set $\left(n \in N:\left(2^{n}-2\right)\right.$ is a multiple of $3\, )$ is equal to:
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is:
  1. Commutative but not associative.
  2. Associative but not commutative.
  3. Neither commutative nor associative.
  4. Both commutative and associative.