Question

Find : $\textstyle\int{\frac{\sin^{6}x}{\cos^{8}x}}\,d x.$

Evaluate $\textstyle\int{\frac{2}{1+\cos2x}}\,d x$

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).

If matrix A = [1 2 3], then write AA’.

If $\begin{vmatrix} 2x & x+3 \\ 2(x+1) & x+1 \end{vmatrix} = \begin{vmatrix} 1 & 5 \\ 3 & 3 \end{vmatrix}$, write the value of x.

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.