Question 1005639
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Cos20°-cos320°+cos100°
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Notice that cos(320°) = cos(40°).

Hence cos(20°) - cos(320°) = cos(20°) - cos(40°).

Now apply the formula {{{cos(alpha) - cos(beta)}}} = {{{-2*sin((alpha+beta)/2)*sin((alpha-beta)/2)}}} 

&nbsp;&nbsp;&nbsp;&nbsp;(see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-of-trigonometric-functions.lesson>Addition and subtraction of trigonometric functions</A>&nbsp; in this site). 

You will get cos(20°) - cos(320°) = cos(20°) - cos(40°) = -2*sin(30°)*sin(10°) = -2*{{{sqrt(3)/2}}}.sin(10°) = -{{{sqrt(3)}}}*sin(10°). 

Next, notice that the last addend, cos(100°) = -sin(10°).

It gives you the final result 

cos(20°) - cos(320°) + cos(100°) = {{{-sqrt(3)}}}*sin(10°) - sin(10°) = -{{{(sqrt(3)+1)}}}.sin(10°).
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