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Show that sin^(-1)frac[12][13]+cos^(-1)f...

Show that `sin^(-1)frac[12][13]+cos^(-1)frac[4][5]+tan^(-1)frac[63][16]=pi`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the value of a and b if the function given below is continuous. ...

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  2. If y=(sinx)^(tanx), find frac[dy][dx]

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  3. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

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  4. Prove that all normals to the curve x = a cos t + at sin t, y = a sin ...

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  5. If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...

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  6. Find intsec^3xdx

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  7. int0^(pi/2)sin2x log(tanx)dx

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  8. Solve (1+x^2)frac[dy][dx]+2xy-4x^2=0 subject to the initial condition ...

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  9. Evaluate: intfrac[x+3][sqrt(5-4x+x^2)]dx

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  10. If with reference to the eight handed system of mutually perpendicular...

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  11. Let veca and vecb be two unit vector and alpha be the angle between th...

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  12. Find the distance between the two planes 2x+3y+4z=4 and 4x+6y+8z=12.

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  13. Solve for x: cot^(-1)(x-1)+cot^(-1)(x-2)+cot^(-1)(x-3)=0

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  14. Show that sin^(-1)frac[12][13]+cos^(-1)frac[4][5]+tan^(-1)frac[63][16]...

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  15. Prove that the following. [[a,b,c],[a^2,b^2,c^2],[bc,ca,ab]]=(b-c)(c-a...

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  16. It is given that for the function f given by f(x)=x^(3)+bx^(2)+ax,x in...

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  17. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  18. Evaluate int0^(frac[pi][2])sin2xcdotlog(tanx)dx

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  19. Evaluate int(sqrt(tan x)+sqrt(cot x))dx

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  20. Prove by vector method that the medians of a triangle are concurrent.

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