Misc 1 - Prove that the Determinant is independent of theta - Evalute determinant of a 3x3 matrix

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Misc 1 Prove that the determinant x sin cos sin x 1 cos 1 x is independent of . Let = x sin cos sin x 1 cos 1 x = x 1 1 sin sin 1 cos + cos sin cos 1 = x ( x2 1) sin ( xsin cos ) + cos ( sin + x cos ) = x3 x + x. sin 2 + sin cos sin cos + x cos2 = x3 x + x sin2 + x+ cos2 + sin cos sin cos = x3 x + x (sin2 + cos2 ) + 0 = x3 x + x (1) = x3 Hence = x3 Which has no term Thus, the determinant is independent of Hence Proved

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.