Question

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ where α and β are acute angles, then write the value of α + β .

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.

Write value of $\textstyle\int$ sec x(sec x + tan x) dx

Write the position vector of the point which divides the join of points with position vectors $3\stackrel{\rightarrow}{a}-2\stackrel{\rightarrow}{b}$ and $2\stackrel{\rightarrow}{a}+3\stackrel{\rightarrow}{b}$ in the ratio 2:1.

Write a unit vector in the direction of the sum of vectors : $\stackrel{\rightarrow}{a}\ = 2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +2\stackrel{\wedge}{k} and \stackrel{\rightarrow}{b}\ = \stackrel{\wedge}{i}+\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$

Using derivative, find the approximate percentage increase in the area of a circle if its radius is increased by 2%.