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Solve the following equation: "cos"("t...

Solve the following equation:
`"cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(4))`.

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Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7))="sin"(4"tan"^(-1)1/(3)) .

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SHARAM PUBLICATION-MODEL QUESTION PAPER -15-EXERCISE
  1. If R and S are two equivalence relation on the set then prove that Rca...

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  2. If ** is a binary operation on set Q of rational numbers such tht a**b...

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  3. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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

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  5. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  6. Solve the following : [[1+x,1,1],[1,1+x,1],[1,1,1+x]]=0

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  7. Eliminate x,y,z from a=x/y-z, b=y/z-x, c=z/x-y

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  8. For what value of lambda,is the function f(x)={(lambdax^2-2x,if xle0),...

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  9. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  10. If y^2cot x = x^2 coty then find (dy)/(dx)

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  11. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  12. Find two positive numbers whose product is 256 and whose sum is least.

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  13. Integrate:inta/(b+ce^x)dx

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  14. Integrate:int sec(sqrtx)/(sqrtx)dx

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  15. Prove that int0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

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  16. Find the area bounded by y=sinx,y=0,x=pi/2

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  17. Solve : (x+y)dy +(x-y)dx = 0.

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  18. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  19. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  20. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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