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If tan^(-1)((x-1)/(x-2))+cot^(-1)((x+2)/...

If `tan^(-1)((x-1)/(x-2))+cot^(-1)((x+2)/(x+1))=(pi)/(4)` , find x.

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Given , `"tan"^(-1)(x-1)/(x-2)+"cot"^(-1)(x+2)/(x+1)=(pi)/(4)`
`"tan"^(-1)(x-1)/(x-2)+"tan"^(-1)(x+1)/(x+2)=(pi)/(4)`
`"tan"^(-1)((x-1)/(x-2)+(x+1)/(x+2))/(1(x-1)/(x-2)xx(x+1)/(x+2))=(pi)/(4)`
`((x-1)(x+2)+(x+1)(x-2))/(((x-2)(x+2))/(((x^(2)-4)-(x^(2)-1))/((x-2)(x+2))))="tan"(pi)/(4)`
`(x^(2)+2x-x-2+x^(2)-2x+x-2)/(x^(2)-4-x^(2)+1)=1`
`(2x^(2)-4)/(-3)=1`
`2x^(2)-4=-3`
`2x^(2)=1`
`x^(2)=(1)/(2)`
`x=+-(1)/(sqrt(2))`
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GURUKUL PUBLICATION - MAHARASHTRA PREVIOUS YEAR PAPERS- OCTOBER 2015-SECTION -II
  1. If tan^(-1)((x-1)/(x-2))+cot^(-1)((x+2)/(x+1))=(pi)/(4) , find x.

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  2. If y=sec^(-1)((sqrt(x-1))/(x+sqrt(x)))+sin^(-1)((x+sqrt(x))/(sqrt(x-1...

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  3. If I=int(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx, then the val...

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  4. The solution of the differential equation (dy)/(dx)=secx-ytanx is :

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  5. Evaluate : int(1)/(xlogxlog(logx))dx

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  6. Find the area of the parabola y^2=4a xbounded by its latus rectum.

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  7. Find k ,such that the function P(x)={{:(k({:(4),(x):}),,x=0","1"...

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  8. Given X~B(n,p).If E(X)=6 and Var (X) = 4.2, find the value of n.

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  9. Solve the different equation y-x(dy)/(dx)=0.

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  10. Discuss the continuity of the following functions at the points shown ...

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  11. If f'(x)=k(cos x-sinx), f'(0)=3, f((pi)/(2))=15, find f(x)

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  12. cos^(-1)((3cosx-2sinx)/(sqrt(13)))

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  13. Show that int(1)/(x^(2)sqrt(a^(2)+x^(2)))dx=(-1)/(a^(2))(sqrt(a^(2)+x...

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  14. A rectangle has an area of 50 "cm"^(2). Find its dimensions for least ...

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  15. int(-a)^(a)f(x)dx= 2int(0)^(a)f(x)dx, if f is an even function 0, if...

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  16. If y =f(u) is differentiable function of u, and u=g(x) is a differenti...

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  17. Each of the total fice questions in amultiple choice examination has f...

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  18. If f(x)=x^(2)+a, for xge0, f(x)=2sqrt(x^(2)+1)+b,"for"xlt0andf((1)/(2...

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  19. Find the approximate values of : cos(89^(@)30)," given "1^(@)=0.0175...

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  20. Solve the different equation : x+y(dy)/(dx)=sec(x^(2)+y^(2)). Also f...

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  21. Find the expected value ,variance and standard deviation of random var...

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