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if 0 lt x lt 1 then tan^(-1)= sqrt(1-x^2...

if `0 lt x lt 1` then `tan^(-1)= sqrt(1-x^2)/(1+x^2)` is equal to (i) `1/2 cos^(-1)x ` (ii)` cos^(-1)sqrt((1+x)/2)` (iii) ` sin^(-1)sqrt((1-x)/2)` (iv) `1/2 tan^(-1)((1+x)/(1-x))`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The solution set of equation sin^(-1) sqrt(1-x^2) + cos^(-1) x = cot^(...

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  2. The solution set of the equation sin^(-1)sqrt(1-x^2)+cos^(-1)x=cot^(-...

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  3. if 0 lt x lt 1 then tan^(-1)= sqrt(1-x^2)/(1+x^2) is equal to (i) 1/...

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  4. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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  5. If [sin^-1x]+[cos^-1x]=0, where 'x' is a non negative real number and ...

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  6. Value of k for which the point (alpha,sin^(-1)alpha)(alpha>0) lies ins...

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  7. Solution set of the inequality sin^(-1)(sin((2x^2+3)/(x^2+1)))lt=pi-5/...

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  8. Consider two geometric progressions a1,a2,a3,......a0 & b1, b2, b3,......

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  9. The sum of the infinite terms of the series cot^(-1)(1^2+3/4)+cot^(-1)...

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  10. If the numerical value of tan{cos^-1(4/5)+tan^-1(2/3)} is a/bthen

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  11. The value of cos[1/2cos^(-1)(cos(-(14pi)/5))]\ is/are a.cos(-(7pi)/...

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  12. Prove that: tan^-1(1/4)+tan^-1(2/9)=1/2 cos^-1(3/5).

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  13. sin^(-1)(3x)/5+sin^(-1)(4x)/5=sin^(-1)x , then roots of the equatio...

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  14. sin^(-1)(sin(33pi)/7)\

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  15. cos^(-1)(cos(46pi)/7)

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  16. tan^(-1)(tan((-33pi)/7))

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  17. cot^(-1)(cot((-46 pi)/7))

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  18. Find value of Sin ( tan^(-1) x)

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  19. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

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  20. sin(cot^(-1)(tan(tan^(-1)x))),"x" in (0," 1]

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