these you can know from looking at the graphs of the trig functions. if you can figure out the values for sine and cosine, you can figure out the rest. so, what is sin(90) and cos(90)? look at the graphs. the angles are on the x-axis and the values of the functions are on the y-axis.

then, you know that:

tan(90) = sin(90)/cos(90)

sec(90) = 1/cos(90)

cosec(90) = 1/sin(90)

cot(90) = 1/tan(90) = cos(90)/sin(90)