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The exact value of tan 5 π/12

The exact value of tan 5 π/12-example-1

1 Answer

3 votes

Answer:

C

Explanation:

Using the addition formula for tangent

tan(x + y) =
(tanx+tany)/(1-tanxtany) and the exact values

tan(
(\pi )/(6) ) =
(1)/(√(3) ) and tan(
(\pi )/(4) ) = 1

tan(
(5\pi )/(12) ) = tan(
(\pi )/(6) +
(\pi )/(4) )

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

=
((1)/(√(3) )+1 )/(1-(1)/(√(3) ).1 ) ( multiply numerator/ denominator by
√(3) )

=
(1+√(3) )/(√(3) -1)

rationalise denominator by multiplying numerator/denominator by (
√(3) + 1)

=
((1+√(3))(√(3)+1) )/((√(3)-1)(√(3)+1) )

=
(√(3)+1+3+√(3) )/(3-1)

=
(2√(3)+4 )/(2)

=
√(3) + 2 → C

User Ahmet K
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