Question 1042402
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Sin 75°+cos 75°
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<pre>
   sin(75°) + cos(75°) =     (use cos(75°) = sin(90°-75°) = sin(15°) )

 = sin(75°) + sin(15°) =     ( use the formula sin(a) + sin(b) = 2*sin({{{(a+b)/2}}})*cos({{{(a-b)/2}}}) )

 = 2*sin(45°)*cos(30°) = 2*{{{sqrt(2)/2}}}*{{{sqrt(3)/2}}} = {{{sqrt(6)/2}}}.
</pre>

Regarding the trigonometry formula, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Compendium-of-Trigonometry-Formulas.lesson>FORMULAS FOR TRIGONOMETRIC FUNCTIONS</A>

in this site.