How do you use a half-angle formula to simplify #tan 75#?

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Answer 1 · 2015-05-27T01:42:26

#tan(75^@) = tan((150^@)/2) = (1-cos(150^@))/sin(150^2)#

The reference angle for #150^@# is #30^@#
and #150^@# is in quadrant 2 so
#cos(150^@)# is negative and #sin(150^@) is positive.

That is #tan(75^@)#

#=(1-cos(150^@))/(sin(150^@))#

#= (1+cos(30^@))/(sin(30^@))#

#= (1+sqrt(3) /2)/(1/2)#

#= 2 + sqrt(3)#