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Prove that tan^(-1) {(sqrt(1+cos x)+sqrt...

Prove that `tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(1-cosx))}=pi/4+x/2`

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UNITED BOOK HOUSE-SET 6-EXERCISE
  1. Solve: (1+x^2)(dy)/(dx) = y+tan^(-1)x

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  2. If vec p is a unit vector and (vec x- vecp).(vec x+ vecp) = 8 then fin...

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  3. Find the intercepts made by the plane x-2y+3z-18=0 on the axes.

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  4. If P(A) = 5/13,P(B)= 6/13 and P(AuuB) = 7//13 then find P(bar A//B) a...

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  5. The mean and variance of a binomial distribution are 16 and 12 respect...

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  6. Prove that tan^(-1) {(sqrt(1+cos x)+sqrt(1-cosx))/(sqrt(1+cos x)-sqrt(...

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  7. Let A = [[1,0],[-1,7]] and I = [[1,0],[0,1]] then find the K when A^2=...

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  8. Show that A = [[1,2,2],[2,1,2],[2,2,1]] satrisfies the matrix equation...

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  9. If alpha,beta,gamma are in A.P. then show that , |[x-3,x-4,x-alpha],[x...

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  10. If sqrt(1-x^6)+sqrt(1-y^6) = a(x^3-y^3) then prove that (dy)/(dx)= x^2...

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  11. If y = (x+ sqrt(1+x^2))^n then prove that (1+x^2)y2+xy1 = n^2y.

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  12. Evaluate: int (dx)/(1+tanx)

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  13. Evaluate: int e^x (2-sin 2x)/(1-cos 2x)dx

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  14. Solve: (x+3)(dy)/(dx)-3y =(x+3)^5

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  15. Solve: y^2dx+(xy+x^2)dy =0

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  16. If vec axx vec b= vec cxxvec d and vec axxvec c= vec bxxvec d, vec a n...

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  17. A and B toss a coin alternately untill one of them gets a head for the...

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  18. Show that the sum of the intercepts of the tangent to the curve sqrtx+...

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  19. Prove that the perpendicular distance of the line 3x+4y+5 =0 from ori...

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  20. If vec a+ vec b+ vec c = vec 0 then prove that vec axx vec b= vec bxx ...

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