.
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 =
(see the lesson Addition and subtraction of trigonometric functions in this site).
You will get cos(20°) - cos(320°) = cos(20°) - cos(40°) = -2*sin(30°)*sin(10°) = -2*.sin(10°) = -*sin(10°).
Next, notice that the last addend, cos(100°) = -sin(10°).
It gives you the final result
cos(20°) - cos(320°) + cos(100°) = *sin(10°) - sin(10°) = -.sin(10°).