evaluate: cos (arc sin (4/5) - arc tan 2) with out using a calc.

Answer 1

cos (arc sin (4/5) - arc tan 2)

remember that arcsin(4/5) and arctan2 are just angles,
so
cos (arc sin (4/5) - arc tan 2)
= cos(arcsin(4/5)cos(arctan2) + sin(arcsin(4/5))sin(arctan2))
= (3/5)(1/√5) + (4/5)(2/√5) = 11/(5√5)