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Solve sin^(-1) x gt tan^(-1) x...

Solve `sin^(-1) x gt tan^(-1) x`

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Verified by Experts

The correct Answer is:
`x in (0,1)`
We have `sin^(-1) x lt tan^(-1) x`
Given inequality is meaningful if `x in [-1, 1]`.
Now, let's draw the graph of `y = sin^(-1) x and y = tan^(-1) x`.

From the graph, we can see that `sin^(-1) x gt tan^(-1) x " for " x in (0, 1]`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  2. Find the value of x for which sin^(-1) (cos^(-1) x) lt 1 and cos^(-1) ...

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  3. Solve sin^(-1) x gt tan^(-1) x

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  4. Find the range of f(x) = cos^(-1) x + cot^(-1) x

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  5. If (sin^(-1)x)^2+(sin^(-1)y)^2+(sin^(-1)z)^2=3/4pi^2 , find the value ...

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  6. Find the value of sin(1/4)cos^(-1)((-1)/9)

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

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  8. Prove that sin^(-1). ((x + sqrt(1 - x^(2)))/(sqrt2)) = sin^(-1) x + (p...

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  9. Find the following values : (a) tan^(-1) (tan13pi/5) (b) sec^(-1)( s...

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  10. If f(x) = sin^(-1) (sin ("log"(2) x)), then find the value of f(300)

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  11. find the maximum value of f(x) = (sin^(-1) (sin x))^(2) - sin^(-1) (si...

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  12. Solve for sin^(-1) (sin 5) gt x^(2) - 4x

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  13. Consider function f(x) = sin^(-1) (sin x) + cos^(-1) (cos x), x in [0,...

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  14. Find the values of x in [0,2pi] for which function f(x) = tan^(-1) (ta...

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  15. Express sin^(-1).(sqrtx)/(sqrt(x + a)) as a function of tan^(-1)

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  16. If tan(cos^(-1) x) = sin (cot^(-1)(1/2)), then find the value of x

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

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  18. Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x...

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  19. tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x)) where x!=0, is equal to

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

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