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Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/...

Prove that:`tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4; m^(2)/n^(2) > -1 `

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Statement 1: If agt0,bgt0, tan^(-1)(a/x)+tan^(-1)(b/x)=(pi)/2 . implies x=sqrt(ab) Statement 2: If m,n epsilonN,ngem, then "tan"^(-1)(m/n)+tan^(-1)(n-m)/(n+m)=(pi)/4 .

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NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. prove that: 2 tan ^(-1).(1)/(3) + tan^(-1).(1)/( 7) = (pi)/(4)

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  2. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  3. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=[pi/4; m^(2)/n^(2) > -1

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  4. Prove that : tan^(-1).(x)/(x+1)- tan ^(-1) (2x +1) = (3pi)/(4)

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

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  6. Prove that : cot^(-1) 3 + cot^(-1).(3)/(4) = cot^(-1) .(1)/(3)

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  7. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  8. If cos^(-1)x+cos^(-1)y+cos^(-1)=pi,p rov et h a tx^2+y^2+z^2+2x y z=1.

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  9. 4tan^(- 1)(1/5)=tan^(- 1)(1/70)-tan^(- 1)(1/99)+pi/4

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  10. Prove that : cos ^(-1) ((1- a^(2))/(1+a^2)) + cos ^(-1)((1-b^(2))/(1...

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  11. tan[1/2 sin^(-1)((2a)/(1+a^2)) + 1/2 cos^(-1)((1-a^2)/(1+a^2))]=

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  12. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((63)/(65...

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  13. Prove that: sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)

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  14. Prove that : cos^(-1).(4)/(5)+ tan ^(-1).(3)/(5) = tan^(-1) .(27)/(11)...

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  15. Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove tha...

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  16. If cos^(-1)(x/2)+cos^(-1)(y/3) = theta, prove that 9x^2- 12xycostheta+...

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  17. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

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  18. Solve : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

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  19. Solve the equation for x : "sin"^(-1)(5)/(x)+"sin"^(-1)(12)/(x)=(pi...

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  20. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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