Question

Sine (45 + x )?

Answer 1

`sin(45^@+x)=sqrt2/2(cosx+sinx)`

Explanation:

Use the `sin` angle addition formula:

`sin(color(red)A+color(blue)B)=sincolor(red)Acoscolor(blue)B+coscolor(red)Asincolor(blue)B`

Here's our expression:

`color(white)=sin(color(red)(45^@)+color(blue)x)`

`=sincolor(red)(45^@)coscolor(blue)x+coscolor(red)(45^@)sincolor(blue)x`

`=sqrt2/2*coscolor(blue)x+sqrt2/2*sincolor(blue)x`

You can factor if you like:

`=sqrt2/2(coscolor(blue)x+sincolor(blue)x)`

Hope this is the answer you were looking for!