Home
Class 12
MATHS
Write the following function in the simp...

Write the following function in the simplest form: `tan^(-1)x/(sqrt(a^2-x^2))`,`|x|lta`

Text Solution

Verified by Experts

`tan ^-1(x/sqrt(a^2-x^2) )`
let` x=asintheta `
`x/a=sintheta rArr theta= sin^-1 (x/a)`
therefore t`an ^-1(x/sqrt(a^2-x^2) )= tan ^-1((asintheta)/sqrt(a^2-a^2sin^2theta) )`
since` x=asintheta `
`= tan ^-1((asintheta)/(asqrt(1-sin^2theta)))`
...
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|17 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Exercise 2.1|14 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.4|25 Videos

  • LINEAR PROGRAMMING

    NCERT ENGLISH|Exercise EXERCISE 12.2|11 Videos

Similar Questions

Explore conceptually related problems

Write the following functions in the simplest form: tan^(-1){x/(sqrt(a^2-x^2))}

Write the following function in the simplest form: tan^(-1)(1/(sqrt(x^2-1))),|x|>1

Write the following function in the simplest form: tan^(-1)((sqrt(1+x^2)-1)/x ), x!=0

Write the following functions in the simplest form: (i) tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a (ii) tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a

tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

Write the following function in the simplest form: tan^-1 sqrt((1-cosx)/(1+cosx))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following function in the simplest form: tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))

Write the following functions in the simplest form: (i) sin^(-1){x/(sqrt(x^2+a^2))} (ii) cos^(-1){x/(sqrt(x^2+a^2))}