Question 1005071
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Using Trigonometry Identities. Simplify the expression into one trigonometric function then evaluate if possible. 

Cos 13pi/18 * Cos pi/18 + Sin 13pi/18 * Sin pi/18
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It is simple.  The key is to apply the subtraction formula for cosines:


Cos({{{13pi/18}}}) * Cos({{{pi/18}}}) + Sin({{{13pi/18}}}) * Sin({{{pi/18}}}) =


    ( use the facts that Cos({{{pi/18}}}) = Cos({{{-pi/18}}}), Sin({{{pi/18}}}) = -Sin({{{-pi/18}}}) )


= Cos({{{13pi/18}}}) * Cos({{{-pi/18}}}) - Sin({{{13pi/18}}}) * Sin({{{-pi/18}}}) = 

    (now apply the subtraction formula for cosines,  see the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A>&nbsp; in this site) 


= cos ({{{13pi/18}}} - {{{pi/18}}}) = cos({{{12pi/18}}}) = cos({{{2pi/3}}}) = {{{-1/2}}}. 


That's all.