How do you write in terms of theta tan(theta-pi/6)? Thanks.

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Answer 1 · 2018-03-01T04:35:52

#color (blue)(tan (theta-pi/6)=(sqrt3 tan theta-1)/(sqrt3+tan theta))#

So we have
#tan (theta-pi/6)#

#color (green)(Tan (A-B)=(tan A-tanB)/(1+tan A tanB) #

Here #A=theta" ,"B=pi/6#

Plugging in values

#tan (theta-pi/6)= (tan theta-tan (pi/6))/(1+tan theta*tan (pi/6))#

#color (red)(tan (pi/6)=1/sqrt3)#

#tan (theta-pi/6)= (tan theta-1/sqrt3)/(1+tan theta*1/sqrt3)#

#tan (theta-pi/6)=((sqrt3 tan theta-1)*cancel (1/sqrt3))/((sqrt3+tan theta)*cancel (1/sqrt3))#

#tan (theta-pi/6)=(sqrt3 tan theta-1)/(sqrt3+tan theta)#

Hope it helps!