Question

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

Answer 1

Explanation:

Start by squaring both sides

cosA+sinA=
`√(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
`(\pi )/(2)`

2A=
`(\pi )/(2)`

A=
`(\pi )/(4)`

`\pi`
`radians=180^o`

A=
`(180^o)/(4)`=
`45^o`