Question
$\cos\Big(2\tan^{-1}\frac{1}{7}\Big)-\sin\Big(4\sin^{-1}\frac{1}{3}\Big)=$
  1. $1$
  2. $0$
  3. $\frac{1}{2}$
  4. $-\frac{1}{2}$

Answer

  1. $0$

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

The number of possible matrices of order $3\times 3$ with each entry $2$ or $0$ is:
The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is
For non$-$singular square matrix $A, B$ and $C $ of the same order $(AB^{-1} C) =$
The function $\text{f(x)}=|\cos\text{x}|$ is:
  1. Everywhere continuous and differentiable.
  2. Everywhere continuous but not differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  3. Neither continuous nor differentiable at $(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  4. None of these.
The probability that in a year of $22^{nd}$ century chosen at random, there will be $53$ Sunday, is
If $\int\frac{1}{(\text{x}+2)(\text{x}^2+1)}\text{ dx}=\text{a}\log|1+\text{x}^2|+\text{b}\tan^{-1}\text{x}+\frac{1}{5}\log|\text{x}+2|+\text{C},$ then
  1. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  2. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
  3. $\text{a}=-\frac{1}{10},\text{ b}=\frac{2}{5}$
  4. $\text{a}=\frac{1}{10},\text{ b}=\frac{2}{5}$
Let R be the relation over the set of all straight lines in a plane such that  $\text{l}_1\text{Rl}_2\Leftrightarrow\text{l}_1\bot\text{l}_2.$ Then, R is:
  1. Symmetric.
  2. Reflexive.
  3. Transitive.
  4. An equivalence relation.
If $\text{f}(\text{x})=\Big(\frac{\text{x}^\text{l}}{\text{x}^\text{m}}\Big)^{\text{l}+\text{m}}\Big(\frac{\text{x}^\text{m}}{\text{x}^\text{n}}\Big)^{\text{m}+\text{n}}\Big(\frac{\text{x}^\text{n}}{\text{x}^\text{l}}\Big)^{\text{n}+1},$ the $f'(x)$ is equal to :
If A and B are two events, then $\text{P}(\overline{\text{A}}\cap\text{B})=$
  1. $\text{P}(\overline{\text{A}})\text{ P}(\overline{\text{B}})$
  2. $1-\text{P}(\text{A})-\text{P}(\text{B})$
  3. $\text{P}(\text{A})+\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
  4. $\text{P}(\text{B})-\text{P}(\text{A}\cap\text{B})$
Area of the region bounded by the curve $y=\tan x$, line $x=\frac{\pi}{4}$ and the $x$-axis is