JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A=\left[\begin{array}{cc}0 & -\tan \left(\frac{\theta}{2}\right) \\ 0 & \tan \left(\frac{\theta}{2}\right)\end{array}\right]\) and \(\left( I _{2}+ A \right)\left( I _{2}- A \right)^{-1}=\left[\begin{array}{ll} a & - b \\ b & a \end{array}\right],\) then \(13\left( a ^{2}+ b ^{2}\right)\) is equal to ...........
- A \(9\)
- B \(13\)
- C \(16\)
- D \(17\)
Answer & Solution
Correct Answer
(B) \(13\)
Step-by-step Solution
Detailed explanation
\(a ^{2}+ b ^{2}=\left| I _{2}+ A \| I _{2}- A \right|^{-1}\) \(=\sec ^{2} \frac{\theta}{2} \times \cos ^{2} \frac{\theta}{2}=1\)
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