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Question

17 cos2xsin7xcos2xdx=f(x)(sinx)7+C, then f(x) is equal to

A
sin x
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B
cos x
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C
tan x
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D
cot x
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Solution

The correct option is C tan x
17 cos2xsin7xcos2xdx=(sec2xsin7x7sin7x)dx=sec2xsin7xdx7sin7dx=I1+I2Now,I1=sec2xsin7dx=tan xsin7x+7tanx cosxsin8x=tan xsin7xI2I1+I2=tan xsin7x+Cf(x)=tanx

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