sinA+cosA=p ,secA+cosecA=q (cosA)^2/[2-2(sinA)^2-(cosecA)^2]=p^2/(2(p^2)-q^2

Answer 1

you don't offer any ideas at all, but maybe this will get you started
p^2 = (sinA+cosA)^2 = sin^2A+2sinAcosA+cos^2A = 1+2sinAcosA
q^2 = (1/cosA+1/sinA)^2 = (sin^2A+cos^2A)/(sin^2Acos^2A) = 1/(sin^2A cos^2A)

cos^2A/[2-2(sinA)^2-(cosecA)^2]
= cos^2A/(2cos^2A - 1/sin^2A)
= (sin^2A cos^2A)/(2sin^2A cos^2A - 1)

See where you can go with that.

Answer 2

please complete the full equation