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Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x...

Prove that `tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x`

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PRADEEP PUBLICATION-MODEL PAPER (1)-EXERCISE
  1. Let f(x)=tanx, -pi/2<x<pi/2 and g(x)=sqrt(1-x^2). Describe gof.

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  2. The range of the function f(x)=(x^2-x)/(x^2+2x) is:

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  3. Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x

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  4. If A=[(-1,1,-1),(3,-3,3),(5,-5,5)] and B=[(0,54,3),(1,-3,-3),(-1,4,4)]...

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  5. Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n...

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  6. Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):}. Show that f is continu...

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  7. If x=(1-t^2)/(1+t^2), y=(2t)/(1+t^2), find (dy)/(dx) at x=2.

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  8. The total cost C(x) and the total revenue R(x) associated with the pro...

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  9. Find the interval of increase and decrease of the function f(x)=log(1+...

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  10. Evaluate int (e^x)dx/(sqrt(5-4e^x-e^(2x)) , x<0.

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  11. By examining the chest X-ray, the probability that TB is detected when...

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  12. If veca=(1,1,1), vecb=(0,1,-1) are two given vectors then find a vecto...

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  13. Find the distance of the point (-1, -5, -10) from the point of interse...

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  14. Mathematics teacher of class XII in a school faced an awkward situatio...

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  15. Mathematics teacher of class XII in a school faced an awkward situatio...

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  16. Evaluate: underset(0)overset(pi//2)int(x)/(sinx+cosx)dx

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  17. Evaluate int (sinx)/(sin4x)dx.

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  18. Maximize Z=6x+3y subject to constraints xge0, yge0, 4x+yge80, x+5yge11...

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  19. Find the shortest distance between the lines.(x-8)/3.(y+9)/-16 = (z-10...

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  20. A window has the shape of a rectangle surmounted by an equilateral tri...

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