give exact value of expression without calculator explain wi

give exact value of expression without calculator. explain with steps please

of each expression without using a calculato 15 7

Solution

cos( tan^-1(15/8) - sin^-1(7/25) )

let x = tan^-1(15/8) ; let y = sin^-1(7/25)

cos(x- y) = cosxcosy +sinxsiny

now tanx = 15/8 ----> cosx =8/17 ; sinx = 15/17

siny = 7/25 ----> cosy = 24/25

cos(x- y) = cosxcosy +sinxsiny

=(8/17)(24/25) + (15/17)(7/25)

= ( 192 + 105)/425

cos(x- y) = 297/425

cos( tan^-1(15/8) - sin^-1(7/25) ) = 297/425