Question

if cosecx-sinx=a^3;secx-cosx=b^3 then a^2b^2(a^2+b^2)

Answer 1

its equal to 1
1/sinx  - sinx=a^3
(1-sin^2x)/sinx= a^3
cos^2x/sinx=a^3
cos^4/3 x/sin^2/3 x  = a^2.   1
similarly secx - cosx=a^3 is equal to
sin^4/3 x/cos^2/3 x=b^2.        2
multiply 1 & 2

a^2*b^2 =sin^2/3 x  *    cos^2/3 x      3
a^2 +  b^2=cos^4/3 x/sin^2/3 x  +   sin^4/3 x/cos^2/3 x = 1/(sin^2/3 x* cos^2/3 x)    4
multiply 3 &  4
a^2b^2(a^2+b^2) =1