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Prove that sum(k=0)^n ^nCk sinKx.cos(n-K...

Prove that `sum_(k=0)^n ^nC_k sinKx.cos(n-K)x=2^(n-1)sin nx`

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The correct Answer is:
(a) `(n^(2)n+2)/(2)`
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MOTION-BINOMIAL THEOREM -Exercise -3 ( Subjective )
  1. Find the coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(1...

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  2. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  3. Let a = (72!)/(36!)^2-1 , then (A) a is odd (B) a is divisible by 7...

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  4. find the sum of the series sum(r=0)^n(-1)^r *"^nCr[1/(2^r)+(3^r)/(2^(...

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  5. Given that (1+x+x^2)^n=a0+a1x+a2x^2+........+a(2n)x^(2n) find the val...

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  6. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  7. Given that (1+x+x^(2))^(n)=a(0)+a(1)x+a(2)x^(2)+......+a(2n)x^(2n), f...

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  8. If n(j(r))=((1-xn)(1-x(n-1))(1-x^(n-2)).......(1-x^(n-r+1)))/((1-x)(1-...

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  9. Prove that sum(k=0)^n ^nCk sinKx.cos(n-K)x=2^(n-1)sin nx

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  10. The expressions 1+x,1+x+x^2,1+x+x^2+x^3.............1+x+x^2+.............

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  11. Find the coefficients of x^(6) in the expansion of (ax^(2) + bx +...

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  12. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax-by+cz)^9

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  13. Find the coefficient of x^2 y^3 z^4 in the expansion of (ax -by +cx...

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  14. If sum(r=0)^(2n)ar(x-2)^r=sum(r=0)^(2n)br(x-3)^ra n dak=1 for all kgeq...

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  15. Show that the integral part in each of the following is odd. n in N. ...

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  16. Show that the integral part in each of the following is even. n in N....

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  17. Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as ...

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  18. The value of .^(n)C(0).^(n)C(n)+.^(n)C(1).^(n)C(n-1)+...+.^(n)C(n)....

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  19. the value of r for which .^(30)Cr.^(20)C0+^(30)C(r-1).^(20)C1.....+^(...

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  20. The value of r for which .^(20)C(r ), .^(20)C(r - 1) .^(20)C(1) + .^...

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