Use the sum and difference identities tan375 degreeSolutiont

Use the sum and difference identities tan(375 degree)

tan ( 375 )

tan 375 = tan (180+180 + 15 ) = tan 15

now , tan 15 = tan (45 - 30)

applying tan (a-b) rule

tan (45 - 30) =( tan 45 - tan 30 ) / ( 1 + tan 45 * tan 30 ) = 1 - 1/sqrt 3 / 1+ 1/sqrt 3

tan 375 = (sqrt 3 - 1 ) / ( sqrt 3 + 1)