Home
Class 12
MATHS
Prove the following: cot^(-1) [(sqrt(1+s...

Prove the following: `cot^(-1) [(sqrt(1+sinx) + sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))] = x/2 ; x in(0,pi/4)`

Text Solution

Verified by Experts

`sqrt(1+sinx)=sqrt(sin^2(x/2)+cos^2(x/2)+2sin(x/2)cos(x/2)`
`=cos(x/2)+sin(x/2)`
`sqrt(1-sinx)=cos(x/2)-sin(x/2)`
`cot^(-1)((cos(x/2)+sin(x/2)+cos(x/2)-sin(x/2))/(cos(x/2)+sin(x/2)-cos(x/2)+sin(x/2)))`
`cot^(-1)cot(x/2)=x/2`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove the following: cot^(-1)[(sqrt(1+sinx )+sqrt(1-sinx))/(sqrt(1+sinx)-\ sqrt(1-sinx))]=x/2,\ x (0,pi/4)

Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))]=

Prove that cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]

Show that : cot^(-1) [(sqrt(1 + sinx) + sqrt(1 - sinx))/(sqrt(1 + sinx) - sqrt(1 - sinx))]= x/2

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2, x in (0,pi/4)

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)

Prove that : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in(0,pi/4)

Prove that : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in(0,pi/4)

Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)