find the maximum value of determinant ( 1 1 1, 1 1+sin theta 1, 1 1 1+cos theta

Let  = 11111+sin θ1111+cos θApplying C1 = C1 - C2  and C2 = C2 - C3Now,  = 001-sin θsin θ10- cos θ1+cos θ=1sin θ . cos θ - 0=sin θ . cos θ=12 . 2 sin θ . cos θ=sin 2θ2Now, maximum value of sin 2θ = 1So, maximum value of sin 2θ2 = 12Hence, maximum value of given  = 12

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The answer is 1/2. On expanding the detrrminant we get sinthetacostheta which can have maximum value of 1/2 as we can convert it into sin2theta which has max value of 1. Here is the solution:
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Please see answer below
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