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Question

Total number of solution of sinx.tan4x=cosx belonging to (0, π) are

A
4
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B
7
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C
8
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D
5
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Solution

The correct option is D 5
sinxtan4x=cosx
sinxsin4x=cosxcos4x
sinxsin4xcosxcos4x=0
cos(x+4x)=0
cos5x=0
5x=π2+kπ
x=π10+kπ5
Thus, 0<π10+kπ5<π
12<k<92
Thus, k = 0, 1,2,3,4
Hence, it has 5 solutions.

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