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Prove that : 2tan^-1 (1/2) + tan^-1 (1/7...

Prove that : `2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)`

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Prove that : 2tan^-1 (1/2) + tan^-1 (1/6) = tan^-1 (27/14)

Prove that : 2tan^-1 (1/4) + tan^-1 (1/3) = tan^-1 (39/37)

Prove that : 2 tan^-1 (1/2) + tan^-1 (1/5) =tan^-1 (23/11)

Prove that : 2 tan^-1 (1/5) + tan^-1 (1/8) = tan^-1(4/7)

Prove that 2 tan^-1 (1/2) + tan^-1 (1/9) = tan ^-1 (39/23)

Prove that : 2 tan^-1(1/5) + tan^-1(1/4) = tan^-1(32/43)

Prove that : 2 tan^-1(1/7) + tan^-1(1/3) = tan^-1(9/13)

Prove that tan^-1 (1/7) + tan^-1 (1/13) = tan^-1 (2/9)

Prove that : 2tan^-1 (1/5) + tan^-1 (7/17) = pi/4

Prove that : 2 tan^-1(1/5) + tan^-1(1/6) = tan^-1(42/67)

MODERN PUBLICATION-MOCK TEST-3-EXERCISE
  1. Solve : xyy'=1+x+y+xy.

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  2. If veca is any vector in space, show that : veca=(veca*hati)hati+(veca...

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  3. Prove that : 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)

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  4. Solve: tan^-1 2x + tan^-1 3x = frac{pi}{4}

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  5. If A=[[2,-1],[-1,2]],show that A^2-4A+3I=0.

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  6. If A=[[2,0,-1],[5,1,0],[0,1,3]], prove that : A^-1=A^2-6A+11I

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  7. Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q)...

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  8. If the function defined by : f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):...

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  9. Differentiate the following w.r.t.x. x^(cot x) + (sin x)^x.

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  10. Evalute : int(5x+3)/sqrt(x^2+4x+10)dx

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  11. Evaluate : int0^pi (xsinx)/(1+cos^2x)dx.

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  12. Evaluate : ∫0^(pi/2)frac{cos^2x}{cos^2x+4sin^2x}dx

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  13. For the differential equation, find the particular solution satisfying...

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  14. Find the vector equation of the line parallel to the line : (x-1)/5=(3...

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  15. Find the equation of the plane passing through the point ( 1, -1 , 2) ...

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  16. A speaks truth in 60% of the cases, while B in 90% of the cases. In wh...

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  17. Consider f: Rrarr [- 5, ∞) given by f(x) = 9x^2 + 6x- 5. Show that f i...

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  18. Consider the binary operations * : R xx R to R and o: R xx R to R def...

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  19. Show that a cylinder of given volume, open at the top, has minimum tot...

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  20. Using integration find the area of region bounded by the triangle wher...

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