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If cos(2sin^(-1)x)=1/9, then find the va...

If `cos(2sin^(-1)x)=1/9,` then find the values of `xdot`

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Let `sin^(-1) x = theta`. Then,
`cos 2 theta = (1)/(9)`
or `1 - 2 sin^(2) theta = 9`
or `1 - 2x^(2) = (1)/(9)`
or `x^(2) = (4)/(9)`
or `x = +-(2)/(3)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sin^(-1)x1+sin^(-1)x2++sin^(-1)xnlt==(npi)/2,n in N ,n=2m+1, mgeq1...

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  2. Find x satisfying [tan^(-1)x]+[cot^(-1)x]=2, where [] represents the g...

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  3. If cos(2sin^(-1)x)=1/9, then find the values of xdot

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  4. Find the value of sin((1)/(2) cot^(-1) (-(3)/(4)))

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  5. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  6. Solve sin^(-1)(1-x)-2s in^(-1)x=pi/2

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  7. Find the number of solution of the equation "cos"(cos^(-1)x)=cos e c(c...

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  8. Find the principal values of the following (i) sin^(-1) (sin 1) (ii...

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  9. Solve sin^(-1) (sin 6x) = x, x in [0,pi]

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  10. Solve sin^(-1)[((2x^2+4)/(1+x^2))]<pi-3

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  11. Find the area bounded by y=sin^(-1)(sinx) and x-axis for x in [0,100pi...

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  12. Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1)...

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  13. Find the principal value of the following cos^(-1) (cos((48pi)/(7)))

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  14. Solve cos^(-1)(cosx)>sin^(-1)(sinx),x in [0,2pi]

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  15. Find the principal values of the following tan^(-1) (tan. (2pi)/(3))

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  16. Find the number of solution of 2tan^(-1)(tanx)=6-x

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  17. Write tan^(-1) x, x gt 0 in the form of other inverse trigonometric fu...

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  18. Find tan^(-1). (x)/(sqrt(a^(2) - x^(2))) in terms of sin^(-1), where x...

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  19. Show that sin (cot^(-1) (tan cos^(-1)x)) =x

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  20. If x<0, then prove that cos^(-1)x=pi-sin^(-1)sqrt(1-x^2)

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