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about to only mathematics

A

`(x)/sqrt(1+x^(2))`

B

x

C

`xsqrt(1+x^(2))`

D

`sqrt(1+x^(2))`

Text Solution

Verified by Experts

`x cos (cos^(-1)(x)/qrt(1+x^(2))+sin^(-1)(1)/sqrt(1+x^(2))`
`=(x^(2))/(sqrt(1+x^(2))[{x cos (cos^(-1)x)+sin(cos^(-1))}^(2)-1]^(1//2)`
`therefore sqrt(1+x^(2))(x^(2)+1-1)^(1//2)=xsqrt(1+x^(2))`
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OBJECTIVE RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS -Section I - Solved Mcqs
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  2. The number of the solutions of the equation 2 sin^(-1) sqrt(x^(2) + x ...

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  3. If alpha, beta and gamma are the three angles with alpha = 2tan^(-1)(s...

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  4. If f(x) = cos^(-1)x + cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then :

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  5. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  6. If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1...

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  7. If tan^(-1)(a/x)+tan^(-1)(b/x)+tan^(-1)(c /x)+tan^(-1)(d/x)=(pi)/(2) t...

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  8. Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...

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  9. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi , prove that: xsqrt(1-x^2)+ysqrt(1...

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  10. If cos^(-1) sqrtp + cos^(-1) sqrt(1 -p) + cos^(-1) sqrt(1 - q) = (3pi)...

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  11. The solution set of the equation sin^(-1)x=2 tan^(-1)x is

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  12. If cot(cos^(-1)x)=sec{tan^(-1)((a)/sqrt(b^(2)-a^(2)))} then x equals

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  13. tan^(-1)[(C(1)x-y)/(c(1)y+x)]+tan^(-1)[(C(2)-C(1))/(1+C(1)C(2))]..+tan...

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  14. about to only mathematics

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  15. Sigma(r=1)^(infty) tan^(-1)(1)/(2r^(2))=t then tan t is equal to

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  16. Let (x,y)be such that sin^(-1)(ax)+cos^(-1)y+cos^(-1)(bxy)=(pi)/(2) ...

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  17. Let f:[0,4pi]->[0,pi] be defined by f(x)=cos^-1(cos x). The number ...

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  18. If (sin^(-1)x+sin^(-1)y)(sin^(-1)Z+sin^(-1)w)=pi^(2) and n(1),n(2),n(3...

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  19. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^2+z^4+4x^2y^2z^2=K(x^...

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  20. Let tan^(-1) y = tan^(-1) x + tan^(-1) ((2x)/(1 -x^(2))), " where " |x...

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