Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 1 Prove that determinant |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| is independent of ΞΈ. Let β = |β 8(π₯&π ππβ‘π&πππ β‘π@βπ ππβ‘π&βπ₯&1@πππ β‘π&1&π₯)| β = x |β 8(βπ₯&1@1&π₯)| β sin ΞΈ |β 8(βsinβ‘ΞΈ&1@cosβ‘ΞΈ&π₯)| + cos ΞΈ |β 8(βsinβ‘ΞΈ&βπ₯@cosβ‘ΞΈ&1)| = x ( βx2 β 1) β sin ΞΈ ( βxsin ΞΈ β cos ΞΈ) + cos ΞΈ (βsin ΞΈ + x cos ΞΈ) = βx3 β x + x sinβ‘γ2 ΞΈγ + π¬π’π§β‘π cos ΞΈ β sin ΞΈ cos ΞΈ + x cos2 ΞΈ = βx3 β x + x sin2 ΞΈ + x cos2 ΞΈ = βx3 β x + x (sin2 ΞΈ + cos2 ΞΈ) = βx3 β x + x (1) = βx3 (As sin2 ΞΈ + cos2 ΞΈ = 1) Hence β = βx3 Which has no ΞΈ term Thus, the determinant is independent of ΞΈ Hence Proved

Miscellaneous

Misc 1
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Misc. 2 Important Deleted for CBSE Board 2022 Exams

Misc 3

Misc 4 Deleted for CBSE Board 2022 Exams

Misc 5

Misc 6 Important Deleted for CBSE Board 2022 Exams

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important Deleted for CBSE Board 2022 Exams

Misc 12 Important Deleted for CBSE Board 2022 Exams

Misc. 13 Deleted for CBSE Board 2022 Exams

Misc 14 Deleted for CBSE Board 2022 Exams

Misc. 15 Important Deleted for CBSE Board 2022 Exams

Misc. 16 Important

Misc 17 (MCQ) Important Deleted for CBSE Board 2022 Exams

Misc 18 (MCQ)

Misc 19 (MCQ) Important

Matrices and Determinants - Formula Sheet and Summary Important

Chapter 4 Class 12 Determinants (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.