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Q.

 If fx=cos(2x)cos(2x)sin(2x)-cosxcosx-sinxsinxsinxcosx, ther 

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a

f(x) attains its minimum at x=0

b

f(x) attains its maximum at x=0

c

f'(x)=0 at more than three points in (-π,π)

d

f'(x)=0 at exactly three points in (-π,π)

answer is A, C.

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Detailed Solution

fx=0cos2xsin2x2cosxcosxsinx0sinxcosx     C1C1-C2fx=2cosxcos3x=cos4x+cos2xf'x=4sin4x2sin2x=2sin2x1+4cos2x=4sinxcosx8cos2x3

f'0+=ve;f'0is+vefx  has a maximum at x=0f'x=0sin2x=0;    cos2x=3/84solutions in -π,πf'x=0sin2x=0                2x=nπ                x=π2,π2

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