Find the exact value for each of the following expressions t

Find the exact value for each of the following expressions: tan 105 degree sin (5 pi/8) sin 70 degree cos 40 degree - cos 70 degree sin 40 degree

Solution

tan(105) = tan(60+45)

This is of the form tan(A+B) which is equal to

(tan A + tan B)/(1-tan A tan B)

So we get

(tan 60 + tan 45)/(1 - tan 60 tan 45)

(Sqrt3 + 1)/(1 - sqrt3)

-(sqrt3 + 1)/(sqrt3 - 1)