If A = [ cos - sin sin cos ] and A + A ' = I , then the value of is:

Question

If $A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}]$ and $A + A' = I$ , then the value of $α$ is:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{π}{3}$

Explanation:

Let $A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}]$

$∴$ $A' = [\begin{matrix} \cos α & \sin α \\ - \sin α & \cos α \end{matrix}]$

$∴$ $A + A' = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}] + [\begin{matrix} \cos α & \sin α \\ - \sin α & \cos α \end{matrix}]$

$\Rightarrow$ $A + A' = [\begin{matrix} 2 \cos α & 0 \\ 0 & 2 \cos α \end{matrix}]$

$I = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

$∴$ $[\begin{matrix} 2 \cos α & 0 \\ 0 & 2 \cos α \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

$∴$ $2 \cos α = 1$

$\Rightarrow$ $\cos α = \frac{1}{2}$

$\Rightarrow$ $α = \frac{π}{3}$

Solution

Q.
If $A = [\begin{matrix} \cos α & - \sin α \\ \sin α & \cos α \end{matrix}]$ and $A + A' = I$ , then the value of $α$ is:

1 $\frac{π}{6}$

2 $\frac{π}{3}$

3 $\frac{3 π}{2}$

4 $π$

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Solution

Q. If A=[cosα-sinαsinαcosα] and A+A'=I, then the value of α is:

1 π6

2 π3

3 3π2

4 π