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

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

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BETTER CHOICE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE (MCQ)
  1. Prove that sin^(-1)""(3)/(5)+sin^(-1)""(4)/(5)=(pi)/(2)

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  2. Prove that cos^(-1)""(3)/(5)+cos^(-1)""(4)/(5)=(pi)/(2)

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  3. Prove that tan^(-1)((sqrt(1-x^(2)))/(1+x))=(1)/(2)cos^(-1)x

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  4. Prove that cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)

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  5. Show that sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)

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

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

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  8. Prove that 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x in[(1)/(2),1]

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  9. Write tan^(-1)((cosx-sinx)/(cosx+sinx)) in simplest form.

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

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  11. Find the value of cos^(-1)(cos""(13pi)/(6))

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  12. Prove that 2tan^(-1)""(1)/(3)+tan^(-1)""(1)/(7)=(pi)/(4)

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  13. Prove that 2tan^(-1)""(1)/(5)+tan^(-1)""(1)/(8)=tan^(-1)""(4)/(7)

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  14. Show that sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)

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  15. Solve: tan^-1 (x+3) + tan^-1 (x-3) = tan^-1 (frac{4}{39}), x>0

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  16. Solve: tan^-1 (x+4) + tan^-1 (x-4) = tan^-1 (frac{4}{67}), x>0

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  17. Prove that tan^(-1)""(1)/(2)+tan^(-1)""(2)/(11)=tan^(-1)""(3)/(4)

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  18. Express tan^(-1)((cosx)/(1-sinx)),-(pi)/(2)ltxlt(pi)/(2) in the simple...

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  19. Prove that 2tan^(-1)""(1)/(5)+tan^(-1)""(1)/(4)=tan^(-1)""(32)/(43)

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

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