# Recent questions tagged q8-2

### If $x+\large\frac{1}{x}$$=2\cos\;\theta and y+\large\frac{1}{y}$$=2 \cos \;\phi$ show that $\large\frac{x^{m}}{y^{n}} - \frac{y^{n}}{x^{m}}$$= 2i \;sin\left ( m\theta -n\phi \right ) ### For the distribution function given by f(x) = \left\{ \begin{array}{l l} 0&\quad\text{x<0}\\ x^{2} & \quad \text{0$$\leq$$x$$\leq$$1$}\\ 1 & \quad \text{x>1} \end{array} \right.$ Find the density function. Also evaluate$p(x\leq0.5)$### By using the properties of determinants show that$ (ii) \quad \begin{vmatrix} 1&1&1 \\ a&b&c \\ a^3&b^3&c^3 \end{vmatrix} = (a-b)(b-c)(c-a)(a+b+c) $### Are the following set of ordered pairs function? If so,examine whether the mapping is injective or subjective$\;\{(a,b)\;:\;a\;$is a person,$b\;$is an ancestor of$a\}$### Let A =$\begin{bmatrix} 1 & -2 & 1\\ -2 & 3 & 1\\ 1 & 1 & 5 \end{bmatrix}$. Verify that $(ii)\big(A^{-1}\big)^{-1}\$

To see more, click for the full list of questions or popular tags.