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Prove that tan^(-1)((cosx)/(1+sinx))=pi/...

Prove that `tan^(-1)((cosx)/(1+sinx))=pi/4-x/2x in [-pi/2,pi/2]`

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SUNSTAR PUBLICATION-P.U BOARD LATEST MODEL QUESTION PAPER - 3 -PART-C
  1. Show that the relation R in the set A={x in Z :0lexle12} is given by R...

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  2. Prove that tan^(-1)((cosx)/(1+sinx))=pi/4-x/2x in [-pi/2,pi/2]

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  3. Using elementary operations, find the inverse of the matrix [(1,2),(2,...

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  4. If y=(sinx)^(cosx)+x^(sinx) find dy/dx.

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  5. If x=a(costheta+logtan(theta/2)) and y=a sin theta," show that "(dy)/(...

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  6. At what points, the function f(x)=sinx-cosx,0ltxlt2pi, attains local m...

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  7. Evaluate int" e"^(x)sinx dx

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  8. Find int(sinx)/(sin(x-a))dx

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  9. Find the area of the region enclosed by the circle x^(2)+y^(2)=a^(2) b...

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  10. Solve (2dy)/(dx)=(y)/(x)+(y^(2))/(x^(2)))

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  11. Show that the points A(2hati-hatj+hatk),B(hati-3hatj-5hatk) and C(3hat...

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  12. Three vectors satisfy the condition veca,vecb and vecc satisfy the con...

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  13. Find the equation of the plane through the line of intersection of the...

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  14. A random variable x has the following probability distribution. D...

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  15. If f:RrarrR defined by f(x)=(4x+3), show that f is invertible and find...

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  16. If A=[(-1,2),(2,3)],B=[(1,-3),(-3,4)] verify that AB-BA is a skew symm...

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  17. If A=[(2,-3,5),(3,2,-4),(1,1,-2)], find A^(-1). Using A^(-1) solve th...

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  18. If y=e^(a cos^(-1)x),-2lexle1, show that (1-x^(2))(d^(2)y)/(dx^(2))-xd...

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  19. Sand is pouring from a pipe at the rate of 12cm^(3)//sec. The falling ...

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  20. Find the integral of 1/(sqrt(x^(2)-a^(2))) with respect to x and evalu...

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