How to prove that cos (80°)+cos(40°)-cos(20°)=0 ?

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Answer 1 · 2017-10-08T08:49:46

See the proof below

To prove

#cos80+cos40-cos20=0#

Apply the following

#cosA+cosB=2cos((A+B)/2)cos((A-B)/2)#

#cos60=1/2#

Therefore,

#cos80+cos40=2cos((80+40)/2)cos((80-40)/2)#

#=2cos60cos20#

#=2*1/2cos20#

#=cos20#

So,

#cos80+cos40-cos20=cos20-cos20=0#

#QED#