Home
Class 12
MATHS
cos^(- 1)sqrt((sqrt(1+x^2)+1)/(2sqrt(1+x...

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

Text Solution

Verified by Experts

`cos^(-1)sqrt(((1+x^2)+1)/(2sqrt(1+x^2))`
Let `x=tantheta`
`1+x^2=1+tan^2theta=secc^2theta`
`=cos^(-1)sqrt((sqrt(sec^2theta)+1)/(2sqrtsec^2theta))`
`=cos^(-1)sqrt((sectheta+1)/(2sectheta))`
`=cos^(-1)sqrt((1+costheta)/2)`
`cos2theta=2cos^2theta-1`
`1+cos2theta=2cos^2theta`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Differential coefficient tan^(-1)((sqrt(1-x^(2)-1))/(x)) with respect to cos^(-1)sqrt((1+sqrt(1+x^(2)))/(2sqrt(1-x^(2))))

show that , (1) /(2) tan ^(-1) x = cos^(-1) sqrt((1+sqrt(1+x^(2)))/(2sqrt(1+x^(2)))).

Value of cos^-1 sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))) , x ge 0 is

Derivative of tan ^(-1) ((sqrt( 1+x^(2))-1)/( x)) w.r.cos ^(-1) sqrt((1+sqrt( 1+x^(2)))/( 2sqrt(1+x^(2)))) is

cos^(-1)((sqrt(1+x)-sqrt(1-x))/(2))

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2