Arc cos 4/5 signifies an angle whose cosine value is 4/5. If we represent this in the form of a triangle, it would be as shown in the figure above. For the same angle Sine value would be 3/5. This means that angle θ= arc cos 4/5, is same as arc sin3/5.

The given expression can thus be written as Sec(-11/3)- Csc arc sin3/5

= Sec(-11/3) – 1/ Sin arc sin3/5

= Sec(-11/3)- 1/(3/5)

= Sec(-11/3) – 5/3