SOLUTION: Use the sum or difference identities to find the exact value of the trigonometric function. tan([23pi]/[12])

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Question 1032966: Use the sum or difference identities to find the exact value of the trigonometric function.
tan([23pi]/[12])
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Look up half angle formulas on Wikipedia.
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
Use the sum or difference identities to find the exact value of the trigonometric function.
tan([23pi]/[12])
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

 =  =  = -tan(15°) = .

sin(15°) =  =   (formula of half argument for sine, see the lesson  Trigonometric functions of half argument  in this site)

=  =  = .


cos(15°) =  =   (formula of half argument for sine, see the lesson  Trigonometric functions of half argument  in this site)

=  =  = .


Therefore,  tan(15°) = .

You can rationalize the denominator in the last expression by multiplying the numerator and the denominator by . You will get 

tan(15°) =  =  =  = .

Finally,   =  =  =   (negative value).

It is your answer. The problem is solved.


See also the lesson  Trigonometric functions of half argument - Examples,  Example 2.


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