Sine (45 + x )?

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Answer 1 · 2018-03-31T06:46:40

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

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!