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If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=...

If `tan^(-1)(sqrt(1+x^2-1))/x=4^0` then `x=tan2^0` (b) `x=tan4^0` `x=tan1/4^0` (d) `x=tan8^0`

A

`x = tan 2^(@)`

B

`x = tan 4^(@)`

C

`x = tan (1//4)^(@)`

D

`x = tan 8^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan^(-1). (sqrt(1 + x^(2)) -1)/(x) = 4^(@) " " (x != 0)`
`rArr (sqrt(1 + x^(2)) -1)/(x) = tan4^(@)`
`rArr sqrt(1 + x^(2)) = 1 + x tan 4^(@)`
`rArr 1 + x^(2) = 2x tan 4^(@) + 1 + x^(2) tan^(2) 4^(@)`
`rArr x = 0 " or " x = (2 tan 4^(@))/(1 - tan^(2) 4^(@)) = tan 8^(@)`
Since `x != 0`, we have `x = tan 8^(@)`
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single)
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  2. There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...

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  3. If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...

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  4. The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...

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  5. tan(pi/4+1/2cos^-1x)+tan(pi/4-1/2cos^-1x), x!=0 is equal to

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  7. Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1)...

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  8. If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+...

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  9. lf asin^-1 x -bcos^-1 x=c,then asin^-1 x +bcos^-1 equal to

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  10. The solution of the inequality "log"(2) sin^(-1) x gt "log"(1//2) cos^...

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  13. If (sin^(-1) x)^(2) - (cos^(-1) x)^(2) = a pi^(2) then find the range ...

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  14. The number of integer x satisfying sin^(-1)|x-2|+cos^(-1)(1-|3-x|)=pi/...

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  15. The number of solutions of the equation cos^(-1)((1+x^2)/(2x))-cos^(-1...

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  16. f(x)=tan^(-1)x+tan^(-1)(1/x);g(x)=sin^(-1)x+cos^(-1)x are identical fu...

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  17. The value of a for which a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1...

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  18. If sin^(-1)(5/x)+sin^(-1)((12)/x)=pi/2, then x is equal to 7/(13) (b)...

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  19. if cos^(- 1)sqrt(p)+cos^(- 1)sqrt(1-p)+cos^(- 1)sqrt(1-q)=(3pi)/4 ,the...

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