Miscellaneous

Chapter 4 Class 12 Determinants
Serial order wise

Get live Maths 1-on-1 Classs - Class 6 to 12

### 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