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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/4m/n >-1(-3pi)/4m/n<-1\ `

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Prove that: "tan"^(-1)(m)/(n)-tan^(-1)((m-n)/(m+n))=(pi)/(4). m, n gt 0

tan^(-1)((n-5)/(n-6))+tan^(-1)((n+5)/(n+6))=(pi)/(4)

tan^(-1)((n)/(n+1))-tan^(-1)(2n+1)=(3 pi)/(4)

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 .

Prove that: sum_(m=1)^(n)tan^(-1)((2m)/(m^(4)+m^(2)+2))=tan^(-1)((n^(2)+n)/(n^(2)+n+2))

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NAGEEN PRAKASHAN-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2a
  1. prove that: 2 tan ^(-1)x =(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/4m/n >-1(-3pi)/4m/n...

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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)) + cos ^(-1)((1-b^(2))/(1+b...

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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)((12)/(5)...

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

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

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

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

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  17. (i) Solve : 4 sin ^(-1) .(5)/(x) + sin ^(-1).(12)/(x)=(pi)/(2) (ii)...

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  18. (i) Slove : tan ^(-1) (x+1)+ tan ^(-1) (x-1)= tan ^(-1). (8)/(31) ...

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  19. The value of tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^...

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  20. Solve tan^-1(1/(1+2x))+tan^-1(1/(1+4x))=tan^-1(2/x^2)

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