दर्शाइए कि -
` sin ^( -1) "" ( 3 ) /(5) - sin ^( -1) "" (8) /(17) = cos ^( -1) "" ( 84) /(85) `.

Explanation

L.H.S. ` = sin ^( -1) "" ( 3 ) /(5) - sin ^( -1) "" ( 8) /(17) `
` = sin ^( -1) [ (3) /(5) sqrt ( 1 - ((8) /(17))^ 2 ) - ( 8 ) /(17) sqrt ( 1 - ((3 ) /(5))^ 2 ) ] `
` = sin ^( -1) [ ( 3 ) /(5) sqrt ( 1 - ( 64 ) /( 289) ) - (8)/(17) sqrt ( 1 - (9) /(25))] `
` = sin ^( -1) [ (3 ) /(5) sqrt ( ( 289 - 64 ) /(289)) - (8) /(17) sqrt( ( 25 - 9)/(25))] `
` = sin ^( -1) [ ( 3 ) /(5) sqrt (( 225) /(289)) - (8) /(17) sqrt ((16)/(25))] `
` = sin ^( -1) [ ( 3 ) /(5) xx ( 15 ) /(17) - ( 8 ) /(17) xx ( 4 ) /(5) ] `
` = sin^( -1 ) [ (45 - 32) /(85)] = sin^( -1 ) [ (13 ) /(85) ] `
` = cos ^( -1) sqrt ( 1 - ((13 ) /( 85))^ 2) " " [sin ^( -1) x = cos ^( -1) sqrt ( 1 -x ^ 2 ) ] `
` = cos ^( -1) sqrt (((85)^2 - (13) ^ 2)/((85) ^ 2 )) = cos ^ ( -1) sqrt ((( 85 + 13 ) ( 85 -13 )) /((85) ^2) `
` = cos ^ ( -1) sqrt ((98 xx 72 ) /((85) ^2)) = cos ^( -1) ( sqrt ( 49 xx 2 xx 9 xx 8 )) /(85) `
` = cos ^( -1) ( sqrt ( 49 xx 16 xx 9 )) /(85) = cos ^ ( -1) [ ( 7 xx 3 xx 4 ) /( 85 ) ] `
` = cos ^( -1) ((84)/(85)) ` = R.H.S.