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[" If "U(n)=int(0)^( pi)(1-cos nx)/(1-co...

[" If "U_(n)=int_(0)^( pi)(1-cos nx)/(1-cos x)dx," where "n" is positive integer or zero,then show that "U_(n+2)+U_(n)=2U_(n)],[" Hence,deduce that "int_(0)^( pi/2)(sin^(2)n theta)/(sin^(2)theta)=(1)/(2)n pi.]

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