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Prove the following: "cos"{tan^(-1){sin(...

Prove the following: `"cos"{tan^(-1){sin(cot^(-1)x)}}=` `sqrt((1+x^2)/(2+x^2))`

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Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) cos"[tan^(-1){"sin"(cot^(-1)x)}]=sqrt((x^2+1)/(x^2+2))

Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2)) =-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3...

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  2. Find the value of a if [(a-b,2a+c),(2a-b,c+d)]=[(-1,5),(0,13)]

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  3. Prove the following: "cos"{tan^(-1){sin(cot^(-1)x)}}= sqrt((1+x^2)/(...

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  4. Find the Cartesian equation of the line which passes through the po...

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  5. If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat ...

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  6. Find | vec x| , if for a unit vector vec a ,\ ( vec x- vec a)*( vec ...

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  7. Find the length of the perpendicular drawn from the origin to the pl...

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  8. Find the vector equation of the plane passing through three points w...

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  9. Write the principal value of tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) .

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  10. Write the value of tan^(-1)[2sin(2cos^(-1)(sqrt(3)/2))] .

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  11. For what value of x is the matrix A=[(0,1,-2),(1,0,3),(x,3,0)] a skew-...

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  12. Using matrices, solve the following system of linear equations: x - ...

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  13. Write the differential equation representing the family of curves y...

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  14. If A(ij) is the cofactor of the element a(ij) of the determinant |(2,-...

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  15. P and Q are two points with position vectors 3 vec a-2 vec b and v...

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  16. Show that the differential equation 2y e^(x/y)\ dx+(y-2x e^(x/ y) ) dy...

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  17. Sketch the graph of y=|x+3| and evaluate the area under the curve ...

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  18. Evaluate: int(x^2+1)/((x-1)^2(x+3))\ dx

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  19. Evaluate: int(xsin^(-1)x)/(sqrt(1-x^2))\ dx

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  20. Using differentials, find the approximate value of f(2. 01), where ...

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