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Prove that for any positive integer k ,...

Prove that for any positive integer `k ,(sin2k x)/(sinx)=2[cosx+cos3x++cos(2k-1)x]dot` Hence, prove that `int_0^(pi/2)sin2x kcotxdx=pi/2dot`

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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Evaluate Lim(n->oo)n^2 int(-1/n)^(1/n) (2006sinx+2007cosx) |x|dx

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  2. Find f(x) if it satisfies the relation f(x) = e^(x) + int(0)^(1) (x...

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  3. Evaluate the definite integral: int(-1/(sqrt(3)))^(1/(sqrt(3)))((x^4)/...

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  4. about to only mathematics

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  5. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

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  6. If n gt 1. Evaluate int(0)^(oo)(dx)/((x+sqrt(1+x^(2)))^(n))

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  7. Let f(x) be a continuous function AA xepsilonR, except at x=0, such th...

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  8. Given that lim(nrarroo) sum(r=1)^(n) (log(e)(n^(2)+r^(2))-2log(e)n)/n ...

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  9. Given that lim(x to 0)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1,...

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  10. Sketch the graph of cos^(-1)(4x^3-3x) and find the area enclosed betwe...

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  11. Consider a square with vertices at (1, 1), (-1, 1), (-1, -1) and (1, -...

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  12. Let [x] denotes the greatest integer function. Draw a rough sketch of ...

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  13. Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x l...

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  14. Find the area of region : {(x,y) : 0 le y le x^(2) + 1, 0 le y le x + ...

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  15. A curve y=f(x) passes through point P(1,1) . The normal to the curv...

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  16. Find the area of the region which contains all points satisfying condi...

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  17. Find the area of the region which is inside the parabola y = - x^(2) +...

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  18. Area bounded by the line y=x, curve y=f(x),(f(x)gtx,AA xgt1) and the l...

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  19. Let C(1) and C(2) be the graphs of the functions y=x^(2) and y=2x, res...

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  20. If [4a2 4a 1 4b2 4b 1 4c2 4c 1] [f-1 f1 f2] = [3a2 + 3a 3b2 + 3b 3c2 +...

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