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Question

Total number of solution of the equation cos4xcosx=sin4xsinx where x[0,π] is

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Solution

cos4xcosx=sin4xsinx
cos4xcosxsin4xsinx=0
cos5x=0
5x=(2n+1)π2
x=(2n+110)π
0xπ
x=π10,3π10,5π10,7π10,9π10

Total number of solutions is 5.

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