InterviewSolution
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InterviewSolution
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Let n be a positive integer if 1le1gt K len such that (sin^(2)nx)/(sin^(2)x)=a_(@)+sum_(1ge i lt klen) a_(1,k) cos 2 (k-1) for all real number x with x not an integer multiple of pi, then the value of a_(1,k) is |
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Answer» `=(sin nx-sin(n+1)x)/(sinx)` `C=cos2x+cos4c+………..+cos2nx` `=(sin nx cos (n+1)x)/(sinx)` `((sin^(2)nx)/(sin^(2)nx))^(2)=((sin n XSIN(n+1)x)/(sinx))^(2)+((sin n cos(n+1)x)/(sinx))^(2)=s^(2)+c^(2)` On the other hand `s^(2)+c^(2)=(sin2x+sin4x+...........sin2nx)^(2)+(cos2x+cos4x+.............+cos2nx)^(2)` `=n+sum_(1le 1lt k le n) (2sin 2 xsin 2 kx +2cos 2 x cos 2kx)` `=nn+2 sum_(1le 1 lt k le n)cos2(k-1)x` `IMPLIES a_(1,k)=2` |
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