SOLUTION: find exact value of [tan(5pi/4)-tan(pi/12)]/1+tan(5pi/4)tan(pi/12)

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Question 590645: find exact value of [tan(5pi/4)-tan(pi/12)]/1+tan(5pi/4)tan(pi/12)
Answer by lwsshak3(11628) About Me  (Show Source):
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find exact value of [tan(5pi/4)-tan(pi/12)]/1+tan(5pi/4)tan(pi/12)
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use tan addition identity: tan (s-t)=(tan s-tan t)/(1+tan s tan t)
For given problem:
[tan(5pi/4)-tan(pi/12)]/1+tan(5pi/4)tan(pi/12)=tan(5π/4-π/12)
=tan(15π/12-π/12)=tan(14π/12)
=tan(7π/6) (ans)