Question

Write the value of $\textstyle\int\!{\frac{2-3\sin x}{\cos^{2}x}}\,d x$.

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

Find the magnitude of each of the vectors $\stackrel{\rightarrow}{a}$ and $\stackrel{\rightarrow}{b}$,having the same magnitude such that the angle between them is 60° and their scalar product is ${\frac{9}{2}}.$

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are unit vectors, then what is the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$, so that ${\sqrt{2}}$ $\stackrel{\rightarrow}{a}\$ -$\stackrel{\rightarrow}{b}\$ is a unit vector ?

Write the equation of tangent drawn to the curve y = sin x at the point (0, 0).

Evaluate x if : $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$