Step-by-step explanation:
Start by squaring both sides
cosA+sinA=[tex]\sqrt{2}[/tex]
[tex]cos^2A+2cosAsinA+sin^2A=2[/tex]
Apply Trig identity
[tex]cos^2x+sin^2x=1[/tex]
2cosAsinA+1=2
2cosAsinA=1
Apply Trig Identity
2cosxsinx=sin(2x)
sin(2A)=1
2A=arcsin1
arcsin(1) is a known value [tex]\frac{\pi }{2}[/tex]
2A=[tex]\frac{\pi }{2}[/tex]
A=[tex]\frac{\pi }{4}[/tex]
[tex]\pi[/tex] [tex]radians=180^o[/tex]
A=[tex]\frac{180^o}{4}[/tex]=[tex]45^o[/tex]
