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Prove that for any positive integer k , ...

Prove that for any positive integer k ,
`(sin2kx)/(sinx) = 2 [cosx+cos3x+"…."+cos(2k-1)x]`.Hence prove that :
`int_(0)^(pi//lamda)sin(2kx). cot x dx = (pi)/(2)`.

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
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  3. Prove that for any positive integer k , (sin2kx)/(sinx) = 2 [cosx+co...

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  5. Let f(x) be a continuous function AAx in R , except at x=0, such that...

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  7. For a natural the following questions : Now answer the following que...

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

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  9. Draw a graph of the function f(x) = cos^(-1) (4x^(3)-3x), x in [-1,1] ...

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  10. Consider a square with vertices at (1,1),(-1,1),(-1,-1),a n d(1,-1)dot...

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  11. If [x] denotes the greatest integer function. Draw a rough sketch of t...

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  12. Find the area of the region bounded by y = f(x), y = |g(x)| and the li...

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  13. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

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  14. Find the area of region {(x,y):0leylex^(2)+1, 0 le y le x+ 1, 0 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 bounded by y = [-0. 01 x^(4) - 0.02 x^(2)], (where [*] ...

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  17. Let ABC be a triangle with vertices A -=(6,,2sqrt3+1))),B-=(4,2)and C-...

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  18. Find the area of the region which is inside the parabola satisfying t...

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

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  20. Consider the curve C: y = sin 2x - sqrt(3)|sinx|, C cuts the x-axis at...

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