Question 868199
<pre>
Using the sum identity:

{{{sin(alpha+beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)}}}

sin(75°) = sin(45°+30°) = sin(45°)cos(30°) + cos(45°)sin(30°) =

{{{(sqrt(2)/2)(sqrt(3)/2)}}}{{{""+""}}}{{{(sqrt(2)/2)(1/2)}}} {{{""=""}}} {{{sqrt(6)/4}}}{{{""+""}}}{{{sqrt(2)/4}}} {{{""=""}}} {{{(sqrt(6)+sqrt(2))/4}}}

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Using the difference identity:

{{{sin(alpha-beta)=sin(alpha)cos(beta)-cos(alpha)sin(beta)}}}

sin(75°) = sin(120°-45°) = sin(120°)cos(45°) - cos(120°)sin(45°) =

{{{(sqrt(3)/2)(sqrt(2)/2)}}}{{{""-""}}}{{{(-1/2)(sqrt(2)/2)}}} {{{""=""}}} {{{sqrt(6)/4}}}{{{""-""}}}{{{(-sqrt(2)/4)}}} {{{""=""}}} {{{sqrt(6)/4}}}{{{""+""}}}{{{sqrt(2)/4}}} {{{""=""}}} {{{(sqrt(6)+sqrt(2))/4}}} 

Edwin</pre>