Prove that ? Cos10°cos20°+Sin45°Cos145°+Sin55°Cos245° = 0

1 Answer
Abhishek K.
May 16, 2018

#LHS=cos10cos20+sin45cos145+sin55cos245#

#=1/2[2cos10cos20+2sin45cos145+2sin55cos245]#

#=1/2[cos(10+20)+cos(20-10)+sin(45+145)-sin(145-45)+sin(245+55)-sin(245-55)]#

#=1/2[cos30+cos10cancel(+sin190)-sin100+sin300cancel(-sin190)]#

#=1/2[sin(90-30)+cos10-sin(90+10)+sin(360-60)]#

#=1/2[cancel(sin60)cancel(+cos10)cancel(-cos10)cancel(-sin60)]#

#=1/2*0=0=RHS#

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