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  • Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 17 maths textbook solution

Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 17 maths textbook solution

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Answer: 0

Hint: Here, we use basic concept of determinant of matrix

Given:     \Delta=\left[\begin{array}{ccc} \sec ^{2} \theta & \tan ^{2} \theta & 1 \\ \tan ^{2} \theta & \sec ^{2} \theta & -1 \\ 12 & 10 & 2 \end{array}\right]

Solution: We know that

                \sec ^{2} \theta-\tan ^{2} \theta=1                ..............(1)

                Applying C_{2}\rightarrow C_{2}-C_{1}

                \begin{aligned} \Delta &=\left[\begin{array}{ccc} \sec ^{2} \theta & \sec ^{2} \theta-\tan ^{2} \theta & 1 \\ \tan ^{2} \theta & \tan ^{2} \theta-\sec ^{2} \theta & -1 \\ 12 & 12-10 & 2 \end{array}\right] \\ \Delta &=\left[\begin{array}{ccc} \sec ^{2} \theta & 1 & 1 \\ \tan ^{2} \theta & -1 & -1 \\ 12 & 2 & 2 \end{array}\right] \end{aligned}[From equation (1)]

                \Delta =0 because according to the property of determinant, if any 2 columns are same then \Delta =0

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