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If sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+c...

If `sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-.....)=pi/2` for `0 lt |x| lt sqrt2` then `x=`

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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Which of the following quantities is/are positive? (a)"cos"(tan^(-1)(t...

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  2. Which of the following is/are a rational number? sin(tan^(-1)3+tan^(-...

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  3. If sin^(- 1)(x-(x^2)/2+(x^3)/4-.....)+cos^(- 1)(x^2-(x^4)/2+(x^6)/4-....

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  4. If we consider only the principal values then the value inverse trigon...

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  5. The number of real solution of the equation sqrt(1+cos2x)=sqrt2 sin^(-...

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

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  7. If |cos^(-1)((1-x^2)/(1+x^2))|<pi/3,t h e n

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  8. If alpha,beta(alpha < beta) are the roots of equation 6x^2+11="" x+3="...

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  9. If 2^((2pi)/sin^(-1)x)-2(a+2)^(pi/sin^(-1)x)+8a<0 for at least one re...

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  10. Which of the following is/are the value of "cos"[1/2cos^(-1)(cos(-(14p...

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  11. 2tan^(-1)(-2) is equal to (a)-cos t^(-1)((-3)/5) (b) -pi+cos^(-1)3...

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  12. If the equation sin^(-1)(x^2+x+1)+cos^(-1)(lambda+1)=pi/2 has exactly ...

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  13. Prove that : cos [ tan^(-1) { sin (cot^(-1) x)}]= sqrt((x^2 +1)/(...

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  14. Find the minimum value of the function f(x)=(pi^2)/(16cot^(-1)(-x))-co...

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  15. Find the range of y=(cot^(-1)x)(cot^(-1)(-x))dot

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  16. If x in [-1,0], then find the value of cos^(-1)(2x^2-1)-2sin^(-1)x

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  17. If 1/(sqrt(2))<x<1 then prove that cos^(-1)x+cos^(-1)((x+sqrt(1-x^2))/...

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  18. Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/4+(cos^(-1)x)/2,""0 <...

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  19. Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x lt oo

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  20. Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

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