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Write tan^(-1) x, x gt 0 in the form of ...

Write `tan^(-1) x, x gt 0` in the form of other inverse trigonometric function

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For `theta = tan^(-1) x, x gt 0 " or " tan theta = x`, we have following right-angled triangle.
From the figure,

`theta = sin^(-1) (x)/(sqrt(1 + x^(2)))`
`= cos^(-1) (1)/(sqrt(1 + x^(2)))`
`= cot^(-1) (1)/(x)`
`= sec^(-1) sqrt(1 + x^(2))`
`= cosec^(-1) (sqrt(1 + x^(2)))/(x)`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  2. Find the number of solution of 2 tan^(-1) (tan x) = 6 - x

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

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

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  5. Prove that sin (cot^(-1) (tan (cos^(-1) x))) = x, x gt 0

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

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  7. Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

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

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

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

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

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

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

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

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

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  16. Prove that 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot

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

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

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

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  20. solve sin^(-1) x le cos^(-1) x

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