Question

[Please, help me. I need it quickly]If cosA+sinA=√2, then prove A=45°.

Answer 1

Step-by-step explanation:

Start by squaring both sides

cosA+sinA=$\sqrt{2}$

$cos^2A+2cosAsinA+sin^2A=2$

Apply Trig identity

$cos^2x+sin^2x=1$

2cosAsinA+1=2

2cosAsinA=1

Apply Trig Identity

2cosxsinx=sin(2x)

sin(2A)=1

2A=arcsin1

arcsin(1) is a known value $\frac{\pi }{2}$

2A=$\frac{\pi }{2}$

A=$\frac{\pi }{4}$

$\pi$ $radians=180^o$

A=$\frac{180^o}{4}$=$45^o$