Question

X=sen45° × cos45° + sen135° × cos135°

Answer 1

$x~=~sen(45^\circ)~+~cos(45^\circ)~+~sen(135^\circ)~+~cos(135^\circ)\\\\\\x~=~sen(45^\circ)~+~cos(45^\circ)~+~sen(180^\circ-135^\circ)~+~\left(\,-cos(180^\circ-135^\circ)\,\right)\\\\\\x~=~sen(45^\circ)~+~cos(45^\circ)~+~sen(45^\circ)~-~cos(45^\circ)\\\\\\x~=~2~.~sen(45^\circ)\\\\\\x~=~2~.~\dfrac{\sqrt{2}}{2}\\\\\\\boxed{x~=~\sqrt{2}}$