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Question

Find the value of determinant.
(i) cosθsinθsinθcosθ
(ii) x2x+1x1x+1x+1

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Solution

(i) cosθsinθsinθcosθ
=(cosθ)(cosθ)(sinθ)(sinθ)=cos2θ+sin2θ=1
(ii) x2x+1x1x+1x+1
=(x2x+1)(x+1)(x1)(x+1)
=x3x2+x+x2x+1(x21)
=x3+1x2+1
=x3x2+2

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