Hello Student,

sec(x)=1/cos(x)

Also, cos(A+B)=cosA*cosB - sinA*sinB

Using these two,

sec(240)=1/cos(240) = 1/cos(pi+60)= 1/(cos180*cos60 - sin180*sin60)

Here, cos 180 = -1, sin180 = 0.

Hence,

the value would be 1/ (-cos60) = 1/(-1/2) = -2.

Hope this answers your question. This can also be done directly with the help of graphs as well.