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Prove that sin^(-1) (cos (sin^(-1) x)) ...

Prove that ` sin^(-1) (cos (sin^(-1) x)) + cos^(-1) (sin (cos^(-1) x))=pi/2 , |x| le 1`

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A DAS GUPTA-Inverse Circular Functions -Exercise
  1. 2sin^(-1) (sqrt(1-x)/2) = cos^(-1)().

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  2. sin^(-1)(3x -4x^(3)) = lambda sin^(-1)x then lambda =.

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  3. The numerical value of tan^(-1) 1+ tan^(-1)2 + tan^(-1)3 =.

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  4. The numerical value of tan^(-1) 1+ tan^(-1) (1/2) + tan^(-1) (1/3) =.

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  5. If x gt 1 then 2tan^(-1)x - tan^(-1) ((2x)/(1-x^(2))) =.

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  6. cos^(-1) (63/65) + 2tan^(-1) (1/5)= sin^(1) ().

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  7. The principal value of cos^(-1) (cos 7pi/6)= .

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  8. The value of sin{tan^(-1) (tan ((7pi)/6) + cos^(-1)(cos ((7pi)/3))} is...

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  9. sin[cot^(-1) {tan(cos^(-1)x)}] is equal to

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  10. 2tan^(-1)x = tan^(-1) 2x/(1-x^(2)) is true if

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  11. If tan^(-1)x+ tan^(-1)y + tan^(-1)z = pi, prove that x + y + z = xyz.

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  12. Prove that : cos^(-1).(3)/(5)+ cos^(-1).(12)/(13) = sin^(-1)((63)/(65...

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  13. If x gt 1 then 1/2 cos^(-1) ((x^(2)-1) /(x^(2)+1)) = tan^(-1).

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  14. If tan^(-1) 1/2 + tan^(-1) a = pi/4 then a = .

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  15. Prove that sin^(-1) (cos (sin^(-1) x)) + cos^(-1) (sin (cos^(-1) x))=...

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  16. If tan^(-1) (sqrt(( 1 +x^(2)) -1)/x) = lambda tan^(-1)x then the val...

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  17. If phi= tan^(-1)(( xsqrt3)/(2k-x)) and psi = tan^(-1) ((2x-k)/(k*sqrt...

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  18. The principal value of cos^(-1)cos ((2pi)/3)+ sin^(-1) sin((2pi)/3) is

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  19. If lambda is a root of x^(2) + 3x + 1 = 0 then tan^(-1) lambda+ tan^(-...

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  20. The equation sin^(-1)x - 3sin^(-1)a =0 has real solutions for x if

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