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

If `sin^-1(x - x^2/2 + x^3/4 - ..... infty) + cos^-1 (x^2 - x^4/2 + x^6/4 - ........infty)= pi/2`
`0 lt absx lt pi/2`, then x is

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CENGAGE PUBLICATION-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? a. sin(tan^(-1)3+tan...

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

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  4. If we consider only the principal values of the inverse trigonometric ...

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  5. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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

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

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  8. The equation 3cos^(-1)x-pix-pi/2=0 has one negative solution, one posi...

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  9. If alpha,beta(alpha < beta) are the roots of equation 6x^2+11x+3="0 , ...

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  10. If 2^(2pi//sin^(-1)x) - 2 (a + 2) 2^(pi//sin^(-1)x) + 8a lt 0 for at l...

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

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  12. 2tan^(-1)(-2) is equal to (a)-cos^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (...

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

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  14. Prove that costan^(-1)sincot^(-1)x=sqrt((x^2+1)/(x^2+2))

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

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

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

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  18. If (1)/(sqrt2) lt x lt 1, then prove that cos^(-1) x + cos^(-1) ((x + ...

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

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

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