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Question

If exp {(tan2x+tan4+tan6+...)loge16}, 0<x<π/4, satisfies the quadratic equation x23x+2=0, then the value of cos2x+cos4x is

A
45
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B
5536
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C
1711
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D
1931
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Solution

The correct option is A 5536
tan2x+tan4x+tan6x+...=tan2x1tan2x
Thus , 16tan2x1tan2x satisfies the quadratic equation
16tan2x1tan2x=1,2
tan2x1tan2x=0,14
Now, 0<x<π40<tanx<1
Hence, tan2x1tan2x=14
5tan2x=1
cos2x=56
cos2x+cos4x=cos2x(1+cos2x)=5536

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