7 Prove that the determinant xsin θcos θ-sin θ-x1cos θ1x is independent of θ 8 Without - Maths - Determinants

Question

7 Prove that the determinant x sin   θ cos  
θ - sin   θ - x 1 cos   θ 1 x is
independent of θ
8 Without expanding the determinant, prove that a a 2 b c b b 2 c a
c c 2 a b = 1 a 2 a 3 1 b 2 b 3 1 c 2 c 3

Aarushi Mishra · Accepted Answer

8aa2bcbb2cacc2abR1→aR1R2→bR2R3→cR3=1abca2a3abcb2b3abcc2c3abc=abcabca2a31b2b31c2c31=a2a31b2b31c2c31C1↔C2=-a3a21b3b21c3c21C1↔C3=1a2a31b2b31c2c3
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7. Prove that the determinant x sin θ cos θ - sin θ - x 1 cos θ 1 x is independent of θ. 8. Without expanding the determinant, prove that a a 2 b c b b 2 c a c c 2 a b = 1 a 2 a 3 1 b 2 b 3 1 c 2 c 3 .