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Prove that "tan"^(-1)((sqrt(1+x^(2))+s...

Prove that
`"tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=pi/(4)+1/(2)"cos"^(-1)x^(2)`.

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Directions Prove the following "tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"cos"x))/(sqrt(1+"cos"x)-sqrt(1-"cos"x)))=pi/(4)+x/(2) , if piltxlt(3pi)/(2) .

SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Solve the following equations "tan"^(-1)1/(3)+"tan"^(-1)1/(5)+"tan"^...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Solve: 2tan^(-1)(sinx)=tan^(-1)(2secx),x!=pi/2.

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  16. Prove that (9pi)/(8) -(9)/(4) sin^(-1)((1)/(3)) =(9)/(4) sin^(-1)((2sq...

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  17. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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

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

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  20. Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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