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Find the value of : "tan"1/2["sin"^(-...

Find the value of :
`"tan"1/2["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y^(2))/(1+y^(2))],|x|lt1,ygt0` and `xylt1`

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Verified by Experts

The correct Answer is:
`(x+y)/(1-xy)`
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NCERT BANGLISH-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(...

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  5. Write the following function in the simplest form : "tan"^(-1)1/(sqr...

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

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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/(sqr...

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

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  10. Find the value of : tan^(-1)[ 2 cos (2 "sin"^(-1)1/2)]

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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 : "tan"1/2["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(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. Find the values of each of the following : If "tan"^(-1)(x-1)/(x-2)+...

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  15. Find the value of : sin^(-1)("sin"(2pi)/3)

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

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  17. Find the values of each of the expression following : tan("sin"^(-1...

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  18. cos^(-1)("cos"(7pi)/6) is equal to

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  19. sin((pi)/3-"sin"^(-1)(-1/2)) is equal to

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  20. tan^(-1)sqrt(3)-cot^(-1)(-sqrt(3)) is equal to

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