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If `"sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^4 +4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Show that: tan^(-1)(a-b)/(1+ab)+tan^(-1)(b-c)/(1+bc)+tan^(-1)(c-a)/(1+...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  20. Prove that: cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)

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