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Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)...

Show that: `tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+ca)=0`.

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Prove statement "tan"^(-1) (a-b)/(1+ab)+"tan"^(-1)(b-c)/(1+bc) +"tan"^-1(c-a)/(1+ca) ="tan"^(-1) (a^2-b^2)/(1+a^2b^2) +"tan"^(-1)(b^2-c^2)/(1+b^2c^2)+"tan"^(-1) (c^2-a^2)/(1+c^2a^2)

Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="tan"^(-1)a-"tan"^(-1) c .

If a gt b gt c gt0 , then prove that cot^(-1) ((ab+1)/( a-b)) + cot^(-1) ((bc + 1)/( b-c)) + cot^(-1) ((ca + 1)/( c.-a)) = 0

Answer any three questions (e) If a gt b gt c gt0 , then prove that cot^(-1) ((ab+1)/( a-b)) + cot^(-1) ((bc + 1)/( b-c)) + cot^(-1) ((ca + 1)/( c'-a)) = pi

Answer any three questions Prove that: 2 tan^(-1) ((1)/(5)) - tan^(-1) ((1)/(4)) = tan^(-1) ((8)/(53))

Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +tan^(-1)((1)/(8)) = (pi)/(4) .

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

Prove that: tan^(-1)(3/4)+tan^(-1)(3/5)-tan^(-1)(8/19)=pi/4

Prove that: tan^(-1)(x)=2tan^(-1)(cosec tan^(-1)x-tan cot^(-1)x)

SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Show that:4(cot^(-1)(3/2)+cosec^(-1)sqrt(26))=pi.

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  2. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

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  3. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

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  4. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

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  5. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

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  6. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  7. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

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  8. In a DeltaABC, if mangleA=90^(@), prove that "tan"^(-1)b/(a+c)+"tan"^(...

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  9. Solve the following equations "tan"^(-1)1/(3)+"tan"^(-1)1/(5)+"tan"^...

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  10. Solve: 3 "sin"^(-1) (2x)/(1+x^2) -4"cos"^(-1) (1-x^2)/(1+x^2) +2 "tan"...

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  11. Solve:"cot"^(-1) 1/(x-1) + "cot"^(-1) 1/x +"cot"^(-1) 1/(x+1) = "cot"^...

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  12. Differentiate y=tan^(-1).(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-...

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  13. Prove the "tan"("tan"^(-1)x +"tan"^(-1) y + "tan"^(-1)z)="cot"("cot"^-...

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  14. Solve : tan^(-1)x+tan^(-1)((2x)/(1-x^2))=pi/2

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  15. Prove statement "tan"^(-1) x +"cot"^(-1)(x+1)="tan"^(-1)(x^2+x+1)

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  16. Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(as...

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  17. Prove the "tan"^(-1) 1/(x+y) + "tan"^(-1) y/(x^2=xy+1) ="tan"^(-1)1/x

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  18. Prove statement "cos"^(-1) 12/13 +2"cos"^(-1) sqrt(64/65) +"cos"^(-1) ...

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  19. Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqr...

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  20. Prove that: tan^(-1)(x)=2tan^(-1)(cosec tan^(-1)x-tan cot^(-1)x)

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