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2sin^(-1) (sqrt(1-x)/2) = cos^(-1)()....

`2sin^(-1) (sqrt(1-x)/2) = cos^(-1)`(_______).

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Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

cos[2sin^(-1)sqrt((1-x)/(2))]

prove that cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

(1) / (2) cos ^ (- 1) x = sin ^ (- 1) sqrt ((1-x) / (2)) = cos ^ (- 1) sqrt ((1 + x) / (2 )) = (tan ^ (- 1) (sqrt (1-x ^ (2)))) / (1 + x)

The number of solutions for the equation 2 sin^(-1)(sqrt(x^(2) - x + 1)) + cos^(-1)(sqrt(x^(2) - x) )= (3pi)/(2) is

sin^(-1)(1/2)+cos^(-1)(1/sqrt2)=?

Show that (i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1

y=sin^(-1)((x)/(sqrt(1+x^(2))))+cos^(-1)((1)/(sqrt(1+x^(2))))

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

A DAS GUPTA-Inverse Circular Functions -Exercise
  1. The numerical value of cos{tan^(-1)(-3) + cot^(-1)(-3)} =.

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

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  3. 2sin^(-1) (sqrt(1-x)/2) = cos^(-1)().

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

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

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

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

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

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

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

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

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  12. 2tan^(-1)x = tan^(-1) 2x/(1-x^(2)) is true if

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

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

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

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

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

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

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

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

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