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Express the value of the following in si...

Express the value of the following in simplest form.
`"tan"{1/(2)"sin"^(-1)(2x)/(1+x^(2))+1/(2)"cos"^(-1)(1-y^(2))/(1+y^(2))}`

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The correct Answer is:
`(x+y)/(1-xy)`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS
  1. Express the value of the following in simplest form. "sin("" cos"^(-...

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  2. Express the value of the following in simplest form. "sin"(2"tan"^(-...

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  3. Express the value of the following in simplest form. "tan"{1/(2)"sin...

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  4. Express the value of the following in simplest form. "sin("" cot"^(-...

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  5. Express the value of the following in simplest form. "tan"^(-1)(x+sq...

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  6. Prove statement "sin"^(-1) 3/5+ "sin"^(-1) 8/17="cos"^(-1) 36/85

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  7. Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

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  8. Prove statement "tan"^(-1) 1/7+ "tan"^(-1)1/13="tan"^(-1) 2/9

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  9. Prove that "tan"^(-1)1/(2)+"tan"^(-1)1/(5)+"tan"^(-1)1/8=pi/(4).

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  10. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

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  11. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  12. Show that "sin"^(-1)(4)/(5) +2"tan"^(-1)(1)/(3) =(pi)/(2).

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  13. Prove statement 4 "tan"^(-1) 1/5 -"tan"^(-1) 1/70 + "tan"^(-1) 1/99 = ...

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  14. Prove that 2"tan"^(-1)(1/(5))+"sec"^(-1)((5sqrt(2))/(7))+2"tan"^(-1)(1...

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

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  16. Prove statement"tan"^2 "cos"^(-1)1/sqrt3 +"cot"^2 "sin"^-1 1/sqrt5 =6

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  17. Prove the following statements "cos"" (tan"^(-1)"(cot"" (sin"^(-1)x)...

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

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

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  20. Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="...

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