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

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

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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS
  1. Prove the following statements "cos"" (tan"^(-1)"(cot"" (sin"^(-1)x)...

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

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

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

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  5. Prove statement "cot"^(-1)(pq+1)/(p-q) +"cot"^-1(qr+1)/(q-r) +"cot"^(-...

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

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

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

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

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

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

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  12. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  13. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  14. If "tan"^(-1)x+"tan"^(-1)y+"tan"^(-1)z=pi/(2), show that xy+yz+zx=1

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  15. If r^2 =x^2 +y^2+z^2, "Prove that" "tan"^(-1) (yz)/(xr) ="tan"^(-1) (...

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

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  17. Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.

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  18. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

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  19. If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.

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  20. Solve for x, cos^(-1)x +sin^(-1)((x)/(2)) =(pi)/(6).

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