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Prove the "sin"^(-1) sqrt((x-q)/(p-q))="...

Prove the `"sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)`sqrt((p-x)/(p-q))="cot"^(-1) sqrt((p-x)/(x-q))`

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Prove that : "tan"^(-1)sqrt((xr)/(yz)) +"tan"^(-1) sqrt((yr)/(yx)) +"...

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  2. If u=cot^(-1)sqrtcos alpha-tan^(-1)sqrt(cosalpha)then prove that sincu...

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  3. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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  4. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

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

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  6. Show that:4(cot^(-1)(3/2)+cosec^(-1)sqrt(26))=pi.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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