Evaluate the following equation exactly cos sin11213 tan11S

Evaluate the following equation exactly: cos (sin^-1(12/13) + tan^-1(1))

cos ( sin^-1 (12/13) + tan^-1 (1) )

let

sin^-1 12/13 =x

sin x = 12 / 13

cos x = 5 / 13

tan ^-1 1 = y

tan y= 1

sin y = 1 / sqrt 2

cos y = 1/ sqrt 2

applying cos (x+y ) formula

cos (x+y) = cos x cos y - sin x sin y

plugging the values we get

cos (x+y) = ( 5/13)(1/sqrt 2 ) - (12/13)(1/sqrt 2)

= 5 / 13 sqrt 2 - 12 / 13 sqrt 2

= -7 / 13 sqrt 2

or - (7 sqrt 2) / 26