Question #2533c

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Answer 1 · 2018-02-14T03:13:48

#-1#

This is based on the double angle formula for #tanx#

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

x, in your problem, is #(7pi)/8#, so your problem is really looking for :

#tan(2((7pi)/8))=(2tan((7pi)/8))/(1-tan^2((7pi)/8))#

#tan(2((7pi)/8))=tan((14pi)/8)=tan((7pi)/4)#

#tan((7pi)/4)=-1#

Answer 2 · 2018-02-14T03:20:33

See the explanation

# [2tan((7pi)/8)]/(1 - tan^2((7pi)/8)#

It is in the form of

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

Which is an identity and is equal to #tan2x#.

So, # [2tan((7pi)/8)]/(1 - tan^2((7pi)/8)#

#= tan(2*(7pi)/8)#

#= tan((7pi)/4)#

Now put #pi = 180°#

We get , #tan(7*180/4)#

#= tan(7*45)#

#= tan (315°)#

Now you can use the tables to find the value of #tan (315°)# which is equal to -1.