सिद्ध करे कि :
`tan((pi)/(4) +(1)/(2) cos^(-1) ""(a)/(b)) +tan((pi)/(4) - (1)/(2) cos^(-1)""(a)/(b)) = (2b)/(2)`

Explanation

माना कि `cos^(1) ""(a)/(b) = theta " "therefore cos theta = (a)/(b)` अब `L.H.S. = tan((pi)/(4) +(theta)/(2)) +tan((pi)/(4) - (theta)/(2))`
` = (1+tan ""(theta)/(2))/(1-tan ""(theta)/(2)) +(1-tan""(theta)/(2))/(1+tan""(theta)/(2))=((1+tan ""(theta)/(2))^(2) +(1-tan ""(theta)/(2))^(2))/(1-tan^(2)""(theta)/2)`
` = (2(1+tan^(2) ""(theta)/(2)))/(1-tan^(2)""(theta)/(2))=(2)/(cos theta) = (2)/(a//b) = (2b)/(a) =R.H.S.`