#color(blue)(sec(theta)*csc(theta)#

We know

#color(green)(sec(theta) =1/cos(theta)#

#color(green)(csc(theta) = 1/sin(theta)#

#color(blue)(sec(theta)*csc(theta) = 1/cos(theta)*1/sin(theta)#

Note apply the Pythagorean identity

#color(green)(cos^2(theta)+sin^2(theta) = 1#

#color(green)(=> sin^2(theta) = (1-cos^2(theta))#

#color(green)(=>sin(theta) = sqrt(1-cos^2(theta))#

Our problem would become

#sec(theta)*csc(theta) = 1/cos(theta)*1/sin(theta)#

#color(blue)(sec(theta)*csc(theta) = 1/cos(theta)*1/sqrt(1-cos^2(theta)#

#color(blue)(sec(theta)*csc(theta) = 1/(cos(theta)sqrt(1-cos^2(theta))#