the equation whoose roots are sec2a & cosec2acan be{where 2 is the power of sec &cosec}.

Sum Of Roots
=(1/sin²a)+(1/cos²a)=(sin²a+cos²a)/(sinacosa)²=4/(sin2a)²=4cosec²2a

Product Of Roots
=(1/sin²a)(1/cos²a)=1/(sinacosa)²=4/(sin2a)²=4cosec²2a

X²-(Sum Of Roots)x+Product Of Roots=0

X²-(4cosec²2a)x+4cosec²2a=0