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Find tan^(-1). (x)/(sqrt(a^(2) - x^(2)))...

Find `tan^(-1). (x)/(sqrt(a^(2) - x^(2)))` in terms of `sin^(-1)`, where `x in (0, a)`

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We have `tan^(-1) (x)/(sqrt(a^(2) - x^(2))) = theta`
From the triangle,
`tan^(-1) (x)/(sqrt(a^(2) - x^(2))) = sin^(-1) (x)/(a)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Find the number of solution of 2tan^(-1)(tanx)=6-x

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

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

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

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

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  6. Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x l...

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

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

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

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

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  12. Find the value of sin^(-1)(sin5)+cos^(-1)(cos10)+tan^(-1){tan(-6)}+cot...

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

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

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  15. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to cot^...

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

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  17. If sin^(-1)x=pi/5, for some x in (-1,1), then find the value of cos^(-...

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  18. If sin(sin^(-1)(1/5)+cos^(-1)x)=1, then find the value of x.

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  19. Solve sin^(-1)xlt=cos^(-1)xdot

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  20. Find the range of f(x)=sin^(-1)x+tan^(-1)x+cos^(-1)xdot

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