Question 1045201
{{{sinA - cosA = 1/4}}}  ===>  {{{sin^2(A) - 2cosA*sinA + cos^2(A) = 1/16}}}

===> {{{- 2cosA*sinA  = 1/16 - 1 = -15/16}}}  (why?)

===> {{{cosA*sinA  =  15/32}}} 

Now {{{secA - cscA = 1/cosA - 1/sinA = (sinA - cosA)/(sinAcosA) = (1/4)/(15/32) = 8/15}}}.