Question #10c5a

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Answer 1 · 2018-01-25T08:01:05

The answer is #tan(75)=(sqrt3+1)/(sqrt3-1)# and #sin(1/12pi)=1/2sqrt(2-sqrt3)#

#"Calculation of tan(75)"#

#tan(75)=tan(30+45)#

#tan(a+b)=(tana+tanb)/(1-tanatanb)#

#tan30=1/sqrt(3)#

#tan(45)=1#

#tan(75)=(1/sqrt(3)+1)/(1-1/sqrt3*1)#

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

#=3.732#

#"Calculation of sin(pi/12)"#

#cos2theta=1-2sin^2theta#

#sin^2theta=(1-cos2theta)/2#

#sintheta=sqrt((1-cos2theta)/2)#

#sin(pi/12)=sqrt((1-cos(2*pi/12))/2)#

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

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

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

#=0.2588#