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Simplify each of the following: tan^(-...

Simplify each of the following:
`tan^(-1)(x+sqrt(1+x^(2))),x in R`

Text Solution

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The correct Answer is:
`(pi)/(4) + (1)/(2) tan^(-1) x`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-INVERSE TRIGONOMETRIC FUNCTIONS-SOLVED PROBLEMS
  1. Simplify each of the following: tan^(-1)(x+sqrt(1+x^(2))),x in R

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  2. Find the values of the following. sin^(-1)"" (- (1)/(2) )

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  3. Find the values of the following: Cos^(-1)(-(sqrt(3))/2)

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  4. Find the values of the following: tan^(-1)(1/(sqrt(3)))

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  5. Find the values of the following: cot^(-1)(-1)

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  6. Evaluate the following. sec^(-1) (-sqrt2)

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  7. Find the values of the following: cosec^(-1)(2/(sqrt(3)))

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  8. Find the values of the following: sin^(-1)("sin"(4pi)/3)

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  9. Find the values of the following: cos^(-1)("cos"(4pi)/3)

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  10. Find the values of the following: tan^(-1)("tan"(4pi)/3)

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  11. Find the values of the following: sin("cos"^(-1)5/13)

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  12. Find the values of the following: tan("Sec"^(-1)25/7)

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  13. Find the values of the following cos("tan"^(-1)24/7)

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  14. Find the values of the following: sin^(2)("Tan"^(-1)3/4)

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  15. Find the values of the following: sin((pi)/2-Sin^(-1)(-4/5))

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  16. Find the value of the following: cos(Cos^(-1)(-2/3)-Sin^(-1)(2/3))

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  17. Show that Sec^(2)(cot^(-1)3)+(Cosec^(2)(tan^(-1)2))=85/36

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  18. Find the value of the following cot^(-1)(1/2)+cot^(-1)(1/3)

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  19. Prove that Sin^(-1)(4/5)+Sin^(-1) 7/25 = Sin^(-1) 117/125.

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  20. If x in (-1,1) prove that 2Tan^(-1)x="Tan"^(-1)(2x)/(1-x^(2))

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  21. sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65)=

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