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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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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS
  1. Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(as...

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

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

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

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

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

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

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

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

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

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

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

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  15. Solve: "tan"^(-1)(x-2)/(x-2) + "tan"^(-1) (x+1)/(x+2)=pi/4

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  16. Solve: "tan"^(-1) 1/(2x+1) +"tan"^(-1) 1/(4x+1) = "tan"^(-1) 2/x^2

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

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

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  19. Solve: "cot"^(-1)(1-x^2)/(2x) = "cosec"^(-1)(1+a^2)/(2a) -"sec"^-1 (1+...

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  20. Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(...

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