Given that #tan (1/2 theta) = -3#. Show that #tan theta = 3/4#.?

1 Answer
Douglas K.
Apr 12, 2018

We know the identity:

#tan(2x) = 2tan(x)/(1-tan^2(x))#

Let #x = 1/2theta#, then #2x = theta#:

#tan(theta) = 2tan(1/2theta)/(1-tan^2(1/2theta))#

Substitute #tan(1/2theta) = -3#:

#tan(theta) = 2(-3)/(1-(-3)^2)#

#tan(theta) = 2(-3)/(-8)#

#tan(theta) = 3/4# Q.E.D.

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