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

1 Answer
Mar 1, 2018

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

Explanation:

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!