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Prove that tan^(-1)sqrt(x) =(1)/(2) cos^...

Prove that `tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)`.

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Prove that: sec^2(tan^(-1)3)-cosec^2(cot^(-1)3)=0

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  2. Evaluate "cos"(2"cos"^(-1)x+"sin"^(-1)x) at x=1/(5), where 0le"cos"^(-...

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  3. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  4. Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

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  5. Prove that: tan^(-1)x+tan^(-1)((2x)/(1-x^2))=tan^(-1)((3x-x^3)/(1-3x^2...

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  6. Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin...

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  7. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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

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  9. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  10. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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  11. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  12. Prove that: cot^(-1)7+cot^(-1)18=cot^(-1)5.

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  13. Prove that: sin^(-1)(3/5)+sin^(-1)(8/17)=tan^(-1)(77/36).

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  14. Prove that sin^(-1)((4)/(5)) +sin^(-1)((5)/(13)) +sin^(-1)((16)/(65)...

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  15. Prove that "tan"^(-1)(1/4)+"tan"^(-1)(2/9)=1/2"tan"^(-1)(4/3).

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  16. Solve equation 3"tan"^(-1)1/((2+sqrt3)) - "tan"^(-1) 1/x ="tan"^(-1) 1...

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

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

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

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  20. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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