without expanding, prove that :- (row wise) |(cosec2 θ cot2 θ 1) (cot2 θ cosec2 θ - Maths - Determinants

Question

without expanding, prove that :- (row wise)
|(cosec2​ θ cot2 θ 1)
(cot2 θ cosec2 θ -1) (42 40 2)| =
0

Jasleen Kaur · Accepted Answer

Dear Student,We have,Let ∆ = cosec2θcot2θ1cot2θcosec2θ-142402Apply, C1→C1-C2-C3∆ = cosec2θ-cot2θ-1cot2θ1cot2θ-cosec2θ+1cosec2θ-142-40-2402Now, 1+cot2θ=cosec2θ∆=cosec2θ-cosec2θcot2θ1cosec2θ-cosec2θcosec2θ-10402∆=0cot2θ10cosec2θ-10402We know that, If all the elements of any particular row or any particular column are zero then the value of the determinant is also zero
As coloumn 1 consists of only zero
Therefore, ∆=0 Regards

without expanding, prove that :- (row wise) |(cosec2​ θ cot2 θ 1) (cot2 θ cosec2 θ -1) (42 40 2)| = 0

without expanding, prove that :- (row wise) |(cosec² θ cot² θ 1) (cot² θ cosec² θ -1) (42 40 2)| = 0