Misc 3 - Chapter 4 Class 12 Determinants (Term 1)
Last updated at May 29, 2018 by Teachoo
Solving by simplifying det.
Example 11 Deleted for CBSE Board 2022 Exams
Example 14 Important Deleted for CBSE Board 2022 Exams
Misc 14 Deleted for CBSE Board 2022 Exams
Ex 4.2, 7 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 9 Important Deleted for CBSE Board 2022 Exams
Misc 6 Important Deleted for CBSE Board 2022 Exams
Ex 4.2, 6 Important Deleted for CBSE Board 2022 Exams
Example 32 Important Deleted for CBSE Board 2022 Exams
Solving by simplifying det.
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