`tan. ( pi)/(8)` का मान ज्ञात करें

Explanation

माना कि `theta = ( pi)/(8) ,` तो `2 theta = ( pi)/(4)`
अब, `tan 2 theta = ( 2tan theta )/( 1- tan ^(2) theta ) `
`= :. tan . ( pi)/(4) = ( 2 tan. ( pi)/(8))/( 1- tan^(2). ( pi)/(8))`
` implies 1= (2 x)/(1-x^(2),` जहाँ `x = tan . ( pi)/( 8)`
`implies 1 - x^(2) = 2 x `
`implies x^(2) + 2x -1= 0`
`implies x = ( -2+-2sqrt(2))/(2) = - 1 + sqrt(2) , -1 - sqrt(2)`
`:. x = tan. ( pi)/(8) = sqrt(2) - 1 ` `[ :' tan. ( pi)/(8) gt 0]`