सिद्ध कीजिए
` cos ^( -1) "" (12 ) /(13) = tan ^(-1) "" ( 5 ) /(12) `

Explanation

` cos ^( -1 ) "" (12 ) /(13 ) = tan ^( -1) "" ( 5 ) /(12) `
माना ` cos ^( -1) "" ( 12 ) /(13) = A " "`...(1)
` rArr (12 ) /(13 ) = cos A `
` therefore sin A = sqrt ( 1 - cos ^2 A ) = sqrt ( 1 - (144) /(169)) = sqrt ((25 ) /( 169)) = sqrt ( ( 25 ) /( 169)) = ( 5 ) / (13) `
` tan A = ( sin A ) /( cos A ) = ( 5//13)/(12//13) = ( 5 ) /(12) `
` therefore A = tan ^( -1) "" ( 5 ) /(12) " " `...(2)
समी. (1 ) तथा (2 ) से, L.H.S. = R.H.S.