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If 2^(2pi//sin^(-1)x) - 2 (a + 2) 2^(pi/...

If `2^(2pi//sin^(-1)x) - 2 (a + 2) 2^(pi//sin^(-1)x) + 8a lt 0` for at least one real x, then find the interval of a

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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. The equation 3cos^(-1)x-pix-pi/2=0 has one negative solution, one posi...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that cos^(-1)x=2sin^(-1)(sqrt (1-x)/sqrt2)

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  15. Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)(x/a) ,-a lt x lt ...

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  16. Prove that: cosec(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-...

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  17. Solve 2cos^(-1)x=sin^(-1)(2xsqrt(1-x^2))

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  18. If cos^(-1)x-cos^(-1)(y/2)=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal...

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  19. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^4+z^4+4x^2y^2z^2=K(x^...

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  20. If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x)...

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