
Andy C. answered 09/15/18
Tutor
4.9
(27)
Math/Physics Tutor
Left side:
cos(90 - T) = cos(90)cos(T) + sin(90)sin(T) =
0* cos(T) + 1 * sin(T) =
sin(T)
tan(180 + T) = tan(180) + tan(T) / [ 1 - tan(180)tanT]
= tan(T) / [ 1 - 0 ]
= tan(T)
sin(T)/tan(T) = cos(T)
Right side:
cos(360-T) = cos(360)cos(T) + sin(360)sin(T)
= 1 * cos(T) + 0 * sin(T)
= cos(T)
both sides are cos(T)
which proves the identity