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Prove that sin^(-1)(63/65)=sin^(-1)(5/13...

Prove that `sin^(-1)(63/65)=sin^(-1)(5/13)+cos^(-1)(3/5)`

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Prove that sin^(-1)(5/13)+sin^(-1)(16/65)=cos^(-1)(4/5)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the equation of the tangent to the curve y=sqrt(3x-2) which is...

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  2. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

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  3. Prove that sin^(-1)(63/65)=sin^(-1)(5/13)+cos^(-1)(3/5)

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  4. Evaluate: int0^(2pi)1/(1+e^(sinx))dx

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  5. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  6. Prove the following: cot^(-1)[(sqrt(1+sinx )+sqrt(1-sinx))/(sqrt(1+sin...

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  7. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  8. Using properties of determinants, prove the following |[x,x+y,x+2y],[x...

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  9. Consider f\ : R+vec[4,oo) given by f(x)=x^2+4 . Show that f is inve...

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  10. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  11. If y^x=e^(y-x), prove that (dy)/(dx)=((1+logy)^2)/(logy)

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  12. Write the cartesian equation of a plane, bisecting the line segment...

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  13. Solve the following differential equation: y\ dx+xlog(y/x)dy=2x\ dy

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  14. Find the particular solution of the following differential equation...

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  15. Write the value of sin[pi/3-sin^(-1)(-1/2)]

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  16. For a\ 2\ xx\ 2\ matrix, A=[a(i j)], whose elements are given by a...

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  17. Evaluate: int1^3(2x^2+5x)dx as limit of a sum

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  18. State the reason for the relation R in the set {1, 2, 3} given by R=...

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  19. Write the value of intsecx\ (secx+tanx)\ dx

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  20. Write the value of int(dx)/(x^2+16)

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