Q.

If  fx=2cos x1012cos x1012cos x then f1π3=

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answer is 2.

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Detailed Solution

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The given function is fx=2cosx1012cosx1012cosx

Expand the determinant as 

fx=2cosx4cos2x-1-12cosx =8cos3x-2cosx-2cosx =8cos3x-4cosx

Differenitate both  sides

f'x=-24cos2xsinx+4sinx

Substitute x=π3

f'π3=-241432+432 =-33+23 =-3

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