Find the maximum value of .


We need to find the maximum value of


Let us find the determinant,



Determinant of 3 × 3 matrices is found as,




So,








Multiply and divide by 2 on right hand side,




[∵, By trigonometric identity, sin 2θ = 2 sin θ cos θ]


We need to find the maximum value of .


We know the range of sine function.


-1 ≤ sin A ≤ 1


Or,


-1 ≤ sin 2θ ≤ 1


∴, maximum value of sin 2θ is 1.


⇒ maximum value of = 1/2


Thus, maximum value of


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