Home
Class 12
MATHS
Prove that:tan^(-1)sqrt(x)=1/2cos^(-1)((...

Prove that:`tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)), x in [0,1]`

Text Solution

Verified by Experts

Let `sqrt(x)=tan thetaimpliestan^(2)theta`
`:. RHS=(1)/(2) cos^(-1)""((1-x)/(1+x)), " " x in [0,1]`
`=(1)/(2) cos^(-1)""((1-tan^(2) theta)/(1+tan^(2)theta))`
`=(1)/(2)cos^(-1)(cos2theta)=(1)/(2)(2theta)`
`=theta=tan^(-1)sqrt(x)=` LHS Hence Proved.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|8 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|44 Videos

  • LINEAR PROGRAMMING

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|9 Videos

Similar Questions

Explore conceptually related problems

prove that tan^(-1)(sqrt(x))=(1)/(2)cos^(-1)((1-x)/(1+x)),x in[0,1]

Prove that: quad tan^(-1)sqrt(x)=(1)/(2)cos^(-1)((1-x)/(1+x)),x in[0,1]

Toprove tan ^(-1)sqrt(x)=(1)/(2)cos^(-1)((1-x)/(1+x))

Prove the following: tan^(-1)sqrt(x)=(1)/(2)cos^(-1)((1-x)/(1+x)),x in(0,1)

Prove that tan^(-1)(sqrt((1-cos x)/(1+cos x)))=(x)/(2)

tan^(-1)(sqrt((a-x)/(a+x)))=(1)/(2)cos^(-1)((x)/(a))

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

Prove that tan^(-1) x =sec^(-1) sqrt(1+x^2)

Prove that: sin{tan^(-1)((1-x^(2))/(2x))+cos^(-1)((1-x^(2))/(1+x^(2)))}=1

Home
Profile