(sinA+cosA)(sinB+cosB)=2⇒sinAsinB+sinAcosB +cosAsinB+cosAcosB=2⇒cosAcosB+sinAsinB +cosAsinB+sinAcosB=2⇒cos(A−B)+sin(A+B)=2
We know that the maximum value of sine and cosine functions is 1, so
cos(A−B)=1 and sin(A+B)=1⇒A−B=0 and A+B=π2⇒A=B=π4⇒C=π2⇒1+sec2(C2)=1+sec2(π4) =3