Without expanding show that: $= ∣ ∣ cos e c^{2} θ {cot}^{2} θ 1 {cot}^{2} θ cos e c^{2} θ - 142402 ∣ ∣ = 0$

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$cos e c^{2} θ = 1 + {cot}^{2} θ$
$D = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + {cot}^{2} θ & {cot}^{2} θ & 1 {cot}^{2} θ & 1 + {cot}^{2} θ & - 1 42 & 40 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$D = 2 ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + {cot}^{2} θ & {cot}^{2} θ & 1 {cot}^{2} θ & 1 + {cot}^{2} θ & - 1 21 & 20 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$c_{2} \to c_{2} + c_{3}$
$D = 2 ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 + {cot}^{2} θ & 1 + {cot}^{2} θ & 1 {cot}^{2} θ & {cot}^{2} θ & - 1 21 & 21 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$D = 0$
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Updated on:21/07/2023

Class 12 MATHS DETERMINANTS

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Question 1 - Select One
The value of $Δ =$ |(cosec^2theta,cot^2theta,1),(cot^2theta,cosec^2theta,-1),(42,40,2)| is
A1
B32
C $tan θ$
D0
Question 1 - Select One
$(1 - {cos}^{2} θ) {cot}^{2} θ$
A ${sec}^{2} θ$
B ${cos}^{2} θ$
C $cos e c^{2} θ$
D ${sin}^{2} θ$

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