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Evaluate the following using compound angle formulae: `tan (-Pi/4 - Pi/6)`

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foxwit | Student, Undergraduate | Salutatorian

Posted July 25, 2013 at 11:17 PM via web

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Evaluate the following using compound angle formulae:

`tan (-Pi/4 - Pi/6)`

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 26, 2013 at 1:12 AM (Answer #1)

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Evaluate `tan(-pi/4 - pi/6)` :

Use `tan(A-B)=(tanA-tanB)/(1+tanAtanB)`

where `A=-pi/4,tanA=-1,B=pi/6,tanB=1/sqrt(3)`

`tan(-pi/4-pi/6)=(tan(-pi/4)-tan(pi/6))/(1+tan(-pi/4)tan(pi/6))`

`=(-1-1/sqrt(3))/(1+(-1)(1/sqrt(3)))`

`=(-1-1/sqrt(3))/(1-1/sqrt(3))*sqrt(3)/sqrt(3)`

`=(-sqrt(3)-1)/(sqrt(3)-1)`

`=(-sqrt(3)-1)/(sqrt(3)-1)*(sqrt(3)+1)/(sqrt(3)+1)`

`=(-4-2sqrt(3))/2`

`=-2-sqrt(3)`

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`tan(-pi/4-pi/6)=-2-sqrt(3)~~-3.73`

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