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Q.

The number of solution of sec x cos 5x+1=0 in the interval 0, 2π is

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answer is 8.

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Detailed Solution

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cos 5x+cos xcos x=2 cos 3x cos 2xcos x=0 24cos3 x-3 cos xcos x2 cos2x-1=0 4 cos2 x-3=0 cos x=32                   cos x=-32 x=π6, 2π-π6             x=5π6 π6, 11π6                     =5π6, 7π6 2 cos2 x-1=0 cos x=12                 cos x=-12 x=π4, 7π4                                       x=3π4, 5π4

Total number of solution =8

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