Question
The value of $\sin \cot ^{-1} x$ :
✓
Answer
(D)
$\sin \cot ^{-1} x$
Suppose $\cot ^{-1} x=\theta \therefore x=\cot \theta$
$\therefore \quad \sin \theta=\frac{1}{\sqrt{1+x^2}}$
or $\sin \theta=\left(1+x^2\right)^{\frac{-1}{2}}$ Hence correct option is (D).
$\sin \cot ^{-1} x$
Suppose $\cot ^{-1} x=\theta \therefore x=\cot \theta$
$\therefore \quad \sin \theta=\frac{1}{\sqrt{1+x^2}}$
or $\sin \theta=\left(1+x^2\right)^{\frac{-1}{2}}$ Hence correct option is (D).
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
If $\text{A} =\displaystyle \begin{bmatrix} -1 &\text{amp; } 0 &\text{amp; }0 \\ 0 &\text{amp; }\text{x} &\text{amp; } 0 \\ 0 &\text{amp; } 0 &\text{amp; }\text{m} \end{bmatrix}$is a scalar matrix then $\text{x}+\text{m}=$
→- 0
- -1
- -2
- -3
A bouquet from $11$ different flowers is to be made so that it contains not less then three flowers. Then the number of the different ways of selecting flowers to from the bouquet.
→A relation R is defined as $R =\{(1,2)\}$ on set $A =$ $\{1,2,3\}$, then R is :
→The equation of the line passing through the points $\text{a}_1\hat{\text{i}}+\text{a}_2\hat{\text{j}}+\text{a}_3\hat{\text{k}}$ and $\text{b}\hat{\text{i}}+\text{b}_2\hat{\text{j}}+\text{b}_3\hat{\text{k}}$ is:
→The value of the $\tan\Big(\cos^{-1}\frac{4}{5}+\tan^{-1}\frac{2}{3}\Big)=$
→- $\frac{6}{17}$
- $\frac{7}{16}$
- $\frac{16}{7}$
- None of these.
Given that $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ and $A^2=31$, then
→If the position vectors of P and Q are $\hat{\text{i}}+3\hat{\text{j}}-7\hat{\text{k}}$ and $5\hat{\text{i}}-2\hat{\text{j}}+4\hat{\text{k}}$ then the cosine of the angle getween $\overrightarrow{\text{PQ}}$ and y-axis is:
→- $\frac{5}{\sqrt{162}}$
- $\frac{4}{\sqrt{162}}$
- $-\frac{5}{\sqrt{162}}$
- $\frac{11}{\sqrt{162}}$
Choose the correct answer from the given four options.
Let F = 3x - 4y be the objective function. Maximum value of F is:
Let F = 3x - 4y be the objective function. Maximum value of F is:
A binary operation * on Z defined by a * b = 3a + b for all a, b ∈ Z, is:
- Commutative.
- Associative.
- Not commutative.
- Commutative and associative.
If $R =\left\{(x, y): x, y \in Z , x^2+y^2 \leq 4\right\}$ is a relation in Z then domain of R is :
→