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Write the following function in the simp...

Write the following function in the simplest form: `tan^(-1)(sqrt(1+x^2)-1)/x , x!=0`

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The correct Answer is:
`1/2tan^(-1)x`
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NCERT GUJARATI-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 2.2
  1. Prove the following : 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x epsilon[1/2,1...

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  2. Prove the following : "tan"^(-1)2/11+"tan"^(-1)7/24="tan"^(-1)1/2

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  3. Prove the following : 2"tan"^(-1)1/2+"tan"^(-1)1/7="tan"^(-1)31/17

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  4. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

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  5. Write the following function in the simplest form: tan^(-1)1/(sqrt(x^2...

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  6. Write the following function in the simplest form: tan^(-1)(sqrt((1-co...

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  7. Write the following function in the simplest form : tan^(-1)((cosx-s...

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  8. Write the following function in the simplest form: tan^(-1)x/(sqrt(a^2...

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  9. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

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  10. Find the values of each of the following : tan^(-1)[ 2 cos (2 "sin"^...

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  11. Find the values of each of the following : cot(tan^(-1)a+cot^(-1)a)

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  12. Find the value of the following: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)...

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  13. Find the values of each of the following : If sin ("sin"^(-1)1/5+"co...

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  14. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4, then find the val...

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  15. Find the values of each of the expression following : sin^(-1)("sin"...

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  16. Find the value of each of the expressions in tan^(-1)("tan"(3pi)/4)

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  17. Find the value of tan(sin^(-1)3/5+cot^(-1)3/2)

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  18. cos^(-1)(cos(7pi)/6)is equal to(a) (7pi)/6 (B) (5pi)/6 (C) pi/3 (D) pi...

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  19. sin(pi/3-sin^(-1)(-1/2))is equal to(A) 1/2 (B) 1/3 (C) 1/4 (D) 1

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  20. tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3))is equal to(A) pi (B) -pi/2 (C) 0 (D...

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