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Prove that 2 tan^(-1) sqrt(b/a) =cos^(-1...

Prove that `2 tan^(-1) sqrt(b/a) =cos^(-1) ((a-b)/(a+b))`

Text Solution

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LHS=`2tan^(-1)sqrt(b/a)`
Let `tan^(-1)sqrt(b/a)=theta`
`sqrt(b/a)=tantheta`
`b/a=tan^2theta`
`2theta`
`cos2theta=(1-tan^2theta)/(1+tan^2theta)`
`2theta=cos^(-1)((1-tan^2theta)/(1+tan^2theta))`
`cos^(-1)((1-(b/a))/(1+(b/a)))`
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