Need Help with Trig Identity Problem - Any Assistance Appreciated!

[Barchie]

Hey all, hope you could help me, would be very gratefull if you could.

Homework Statement

Show that sin(x) + cos(x) = √2sin(x + π/4)

Homework Equations

sin(x+z) = sin(x)cos(z)+sin(z)cos(x)

The Attempt at a Solution

Ive been doing some of these trig identity problems without an issue, but i get stuck when it comes to this one.

I get as far as sin(x)cos(45) + cos(x)sin(45)

i have realized that cos(45) and sin(45) when added together happen to = √2 but i can't seem to find the next step :-(

Any help grealy appreciated.

 

[rasmhop]

i have realized that cos(45) and sin(45) when added together happen to = √2 but i can't seem to find the next step :-(

This is true, but do you know an expression for cos(45)? Or for sin(45)? If you find such an expression and substitute it you should be almost done.

BTW you really should work either in degrees or radians and not mix them. pi/4 suggests you work in radians, but 45 suggests you work in degrees.

 

[Barchie]

Legend! Totally looked past that. Much appreciated!

 

[LoopQG]

you are so close

remember sin(45)=cos(45)=1/sqrt(2)

so sin(x+45)=1/sqrt(2) [sin(x) +cos(x)]

 

[Barchie]

Thanks dude :-) Got the answer now! Appreciate the response.