InterviewSolution
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InterviewSolution
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If `cos^3xsin2x=sum_(r=0)^n a_xsin(r x),AAx in R` thenA. `n=5,a_(1)=1//2`B. `n=5,alpha_(1)=1//4`C. `n=5,a_(2)=1//8`D. `n=5,a_(2)=1//4` |
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Answer» Correct Answer - B `cos^(3)xsin2x=cos^(2)x cos x sin 2x` `=((1+cos 2x)/(2))(2sin2xcosx)/(2))` `=(1)/(4)(1+cos 2x)(sin3x+sinx)` `=(3)/(4)[sin3x+sinx+(1)/(2)(2sin 3xcos2x)` `=(1)/(2)(2cos 2xsin x]` `=(1)/(4)[sin3x+sinx+(1)/(2)(sin5x+sinx)+(1)/(2)(sin3x-sinx)]` `=(!)/(4)[sinx+((3)/(2))sin3x+((1)/(2))sin5x]` `rARr a_(1)=1//4,a_(3)=3//8,n=5` |
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