Verifying Sum Difference Formula Results

[aisha]

Using the sum difference formula I got the following

$$\sin(30 degrees +45 degrees)=sin 30 cos45+cos 30 sin 45$$

I used the special triangles and got

$$(\frac {1}{2})(\frac {1}{\sqrt2})+(\frac {\sqrt3}{2}) (\frac {1}{\sqrt2})$$

I rationalized the denominator and got
$$\frac {\sqrt2+\sqrt6} {4}$$

Did i make any errors? Can someone please verify.

 

[Curious3141]

Absolutely correct, well done.

 

[aisha]

Thanks curious