MCQ
यदि $A =\left[\begin{array}{cc}\sin ^2 \theta & \sec ^2 \theta \\ \operatorname{cosec}^2 \theta & \frac{1}{2}\end{array}\right]$ तथा $B=\left[\begin{array}{cc}\cos ^2 \theta & -\tan ^2 \theta \\ -\cot ^2 \theta & \frac{1}{2}\end{array}\right]$ हो, तो A + B का मान होगा-
  • A
    $\left[\begin{array}{cc}1 & -1 \\ 1 & 1\end{array}\right]$
  • B
    $\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right]$
  • C
    $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
  • $\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$

Answer

Correct option: D.
$\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$
(D) $\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$
$\begin{array}{l} A + B =\left[\begin{array}{cc}\sin ^2 \theta & \sec ^2 \theta \\ \operatorname{cosec}^2 \theta & \frac{1}{2}\end{array}\right]+\left[\begin{array}{cc}\cos ^2 \theta & -\tan ^2 \theta \\ -\cot ^2 \theta & \frac{1}{2}\end{array}\right] \\ A+B=\left[\begin{array}{cc}\sin ^2 \theta+\cos ^2 \theta & \sec ^2 \theta-\tan ^2 \theta \\ \operatorname{cosec}^2 \theta-\cot ^2 \theta & \frac{1}{2}+\frac{1}{2}\end{array}\right]=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]\end{array}$
अतः सही विकल्प (D) है।

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