Verified answer

а) (sint+cost)^2/(1+2sin t cos t)=(sin^2t+2sint cost+cos^2t)/(1+2sint cost)=(1+2sint cost)/(1+2sint cost)=1

b) (1-2sin t cos t)/(cos t-si t)^2=(1-2sint cost)/(cos^2t-2sint cost+sin^2t)=(1-2sint cost)/(1-2sint cost)=1

a)  cos^2 t/1-sin t   -sint t=1 

((1-sin^2t)-sint(1-sint))/(1-sint)=1

(1-sin^2t-sint+sin^2t)/(1-sint)=1

(1-sint)/(1-sint)=1