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Question

Let f(x)=tanxtan3x+tan5xtan7x+ , where x(0,π4),

then which of the following is/are correct ?

A
π60f(x)dx=18
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B
f(π12)=12
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C
limx0+f(x)x=1
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D
f(x) is an odd function
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Solution

The correct options are
A π60f(x)dx=18
C limx0+f(x)x=1
D f(x) is an odd function
f(x)=tanxtan3x+tan5xtan7x+....=tanx1+tan2x=sin(2x)2limx0+f(x)/x=sin(2x)2x=1sin(x)isanoddfunctionsin(x)=sin(x)π60sin(2x)2=18
Hence, options 'A', 'C' and 'D' are correct.

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