How do you simplify cos (5pi/12)+cos(2pi/3-pi/4)?

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Answer 1 · 2016-10-07T10:33:32

#cos( (5pi)/12)+cos((2pi)/3-pi/4)#

#=cos( (5pi)/12)+cos((8pi-3pi)/12)#

#=2cos( (5pi)/12)#

#=2 sqrt (1/2(1+cos( (5pi)/6))#

#=sqrt (4xx1/2(1+cos(pi-pi/6))#

#=sqrt (2(1-cos(pi/6))#

# = sqrt (2(1-sqrt3/2)#

# = sqrt(2-sqrt3)#

# = sqrt(1/2(4-2sqrt3))#

# = sqrt(1/2((sqrt3)^2+1^2-2sqrt3*1))#

# = sqrt(1/2(sqrt3-1)^2#

# = ((sqrt3-1))/sqrt2#