समीकरण को हल कीजिए -
` tan ^( -1) (x + 1 ) + tan ^( -1) (x - 1) = tan ^( -1) (( 6 ) /(17)) `

Explanation

दिया है : ` tan ^( -1) ( x + 1 ) + tan ^( -1) ( x - 1) = tan ^( -1) ((6 ) /(17)) `
` rArr tan ^( -1) [ (( x + 1) + (x -1))/( 1 - (x + 1 ) ( x -1)) ] = tan ^( -1) (( 6 ) /(17)) `
` rArr (2x ) /(1 - (x ^ 2 - 1 ) ) = ( 6 ) /(17) `
` rArr ( 2x ) /( 2 - x ^ 2 ) = ( 6 ) /(17) `
` rArr ( x ) /( 2 - x ^ 2 ) = (3) /(17) `
` rArr 17 x = 6 - 3 x ^ 2 `
` rArr 3 x ^ 2 + 17 x - 6 = 0 `
` rArr 3 x ^ 2 + 18 x - x - 6 = 0 `
` rArr 3x ( x + 6 ) - 1 ( x + 6 ) = 0 `
` rArr ( x + 6) ( 3x -1) = 0`
` therefore x = - 6, x = (1)/(3) `