# Misc 3 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 3 (Method 1) Evaluate cos cos cos sin sin sin cos 0 sin cos sin sin cos cos cos cos sin sin sin cos 0 sin cos sin sin cos Expanding Determinant along C1 = cos cos cos 0 sin sin cos cos sin sin 0 sin cos sin sin cos sin sin sin = cos cos (cos cos 0) cos sin ( sin cos 0) sin ( sin2 sin cos2 sin ) = cos cos ( cos cos ) cos sin ( sin cos ) + sin2 sin2 + cos2 sin2 = cos2 cos2 + cos2 sin2 + sin2 ( sin2 + cos2 ) = cos2 (1) + sin2 (1) = cos 2 + sin2 = 1 Misc 3 (Method 2) Evaluate cos cos cos sin sin sin cos 0 sin cos sin sin cos Let = cos cos cos sin sin sin cos 0 sin cos sin sin cos = cos sin cos sin sin cos 0 cos sin sin .cos Taking common cos from R1 & sin from R3 = cos .sin cos sin tan sin cos 0 cos sin co Applying R1 R1 R3 = cos .sin cos sin tan sin cos 0 cos sin co Expanding determinant along R1 = cos . sin 0 cos 0 sin cot 0 sin 0 cos cot (tan cot ) sin cos cos sin = cos . sin 0 0 (tan cot ) sin cos cos sin = cos sin ( (tan + cot ) ( sin2 cos2 )) = cos sin ( tan + cot ) (sin2 + cos2 ) = cos sin (tan + cot ) (1) = cos sin sin cos + cos sin = cos sin + cos sin = cos sin cos (1) = 1

Miscellaneous

Misc 1

Misc. 2 Important Deleted for CBSE Board 2021 Exams only

Misc 3 You are here

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important Deleted for CBSE Board 2021 Exams only

Misc 12 Important Deleted for CBSE Board 2021 Exams only

Misc. 13 Deleted for CBSE Board 2021 Exams only

Misc 14 Deleted for CBSE Board 2021 Exams only

Misc. 15 Important Deleted for CBSE Board 2021 Exams only

Misc. 16 Important

Misc 17 Important Deleted for CBSE Board 2021 Exams only

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

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.