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Prove that cos^(-1)(frac[b+acosx][a+bcos...

Prove that `cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a+b])tanfrac[x][2])`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that int0^(pi)frac[xdx][1+sinx]=pi

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  2. Find the solution of the following differential equations: (2x+3y-5)dy...

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  3. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  4. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

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  5. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

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  6. Using vector method prove that cosA=(b^2+c^2-a^2)/(2bc)

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  7. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  8. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

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

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  10. Solve the following system of equations by matrix method x+2y+3z=8, 2x...

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  11. Find the distance between the parallel planes 2x-2y+z+1=0 and 4x-4y+2z...

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  12. If y=x^(-1)sincosec^(-1)frac[1][x], then what is frac[dy][dx]?

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  13. Write down the smallest and the largest equivalence reaction on a set ...

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  14. Differentiate twice intsin^(-1)xdx+intcos^(-1)xdx

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  15. If x+y=4, xy=1 then what is the value of tan^(-1)x+tan^(-1)y?

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  16. What is the value of hata*hatb+hatb*hatc+hatc*hata if hata+hatb+hatc=v...

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  17. What is the value of abs[[a,b+c,1],[b,c+a,1],[c,a+b,1]] ?

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  18. If A is a 2xx2 non-singular matrix and absA=1/2 then which matrix is r...

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  19. Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.

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  20. What is the value of int0^2abs{x-1)dx?

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