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If A=((cosx,sinx),(-sinx,cosx)) then pro...

If `A=((cosx,sinx),(-sinx,cosx))` then prove that `A^n=((cosnx,sin nx),(-sin nx,cosnx)` for all positive integers n.

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  2. Exaniming consistency and solvability, solve the following equations b...

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  3. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  4. Find dy/dx x=cos^(3)t/sqrtcos2t, y=sin^(3)t/sqrt cos2t

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  5. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  6. Integrate : int(ln (x+√(x^2 + a^2))dx.

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  7. Solve the following differential equations (dy)/(dx)+2ytan x= sin x,...

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  8. Find the area of the région on closed between y = 4x-1 and y^2=2x

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  9. Find the distance of the point (3,-4,5)from the plane 2x+5y-6z-19=0 me...

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  10. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  11. Let f: RrarrR defined by f(x)=x+1 and g:R rarr R defined as g(x)= sqrt...

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  12. Solve cos(2sin^(-1)x) = 1/9.

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  13. Find x and y if [[1,3],[2,-1]][[x],[y]] = [[4],[1]].

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  14. Fill in the blanks with appropriate answer from the brackes. If [[a,b...

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  15. What is the slope of the normal to the curve x^(2/3)+y^(2/3)=20 at the...

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  16. What is the value of int0^(pi/2)log tan x dx?

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  17. Write the general solution of (ydx-xdy)/y=0.

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  18. Write the distance between the plane x-2y+z=6 and 2x-4y+2z=8

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  19. What is the image of the point (6, 3, -4) with respect to yz- plane ...

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  20. Check if the relation R on set of real numbers, defined as R = {(a,b) ...

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