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

Prove that `tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x`.

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UNITED BOOK HOUSE-QUESTION PAPER 2015-EXERCISE
  1. Find out the mean and variance of the following probability distributi...

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  2. Find the probability that birthdays of any two members out of five me...

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  3. Prove that tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x.

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  4. If A = ([1,4],[2,3]) then show that A^2-4A-5I = theta and using this f...

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  5. Solve the following equations by Cramer's method: x+y=1,y+z= 2,x+z=3.

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  6. Show that |[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3.

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  7. Solve for x: |[x,c+x,b+x],[c+x,x,a+x],[b+x,a+x,x]|=0

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  8. Find (dy)/(dx) where x= cos^(-1)(8t^4-8t^2+1) y =sin^(-1)(3t-4t)^3...

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  9. Evaluate: int(2^xdx)/sqrt(4^x-2^(x+2)+5)

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  10. Evaluate : int (3x+5)/(x^3-x^2-x+1)dx

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  11. SolveL (1+y)^2dx=(tan^(-1)y-x)dy, given that y= 0 when x= -1.

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  12. If the rate of increase of population is 5% per year, then in how man...

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  13. Find vecc, when vecaxxvecc=vecb and veca.vecc= 3 where veca= hatr+hatj...

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  14. Find the value of lambda if three vectors veca= 2hati-hatj+hatk,vecb= ...

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  15. Evaluate (with the help of definite integral) underset(n rarr infty)...

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  16. Find the value of overset(pi/2)underset(0)int(x sinx cos x)/(a^2cos^2 ...

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  17. Sum and product of mean and standard deviation of a bionomial distribu...

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  18. The probability distribution of a random variable X is given as follo...

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  19. A lamp is on the top of a lamp post of height 2a metres situated on a ...

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  20. If the line x cos alpha+y sin alpha= p touches the curve x^my^n= a^(m+...

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