Math%112%–%Perfect%problem%7%
Due%Monday%6/1%in%class%
“Best”%solutions%get%extra%credit%
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tan a + tanb
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1− tan a tanb
2 tan x
1) Use%this%to%prove%the%double%angle%formula,%that% tan ( 2x ) =
.%Hint:% tan ( 2x ) = tan ( x + x ) %%
1− tan 2 x
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2) Use%the%angle%addition%formula%and%the%result%from%part%1%to%prove%the%triple%angle%formula,%
3tan x − tan 3 x
that% tan ( 3x ) =
.%Hint:% tan ( 3x ) = tan ( 2x + x ) %%
1− 3tan 2 x
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3) Use%the%angle%addition%formula%and%the%result%from%part%1%to%prove%the%quadruple%angle%formula,%
4 tan x − 4 tan 3 x
that% tan ( 4x ) =
.%Hint:% tan ( 4x ) = tan ( 2x + 2x ) %%
1− 6 tan 2 x + tan 4 x
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4) Use%the%angle%addition%formula%and%the%result%from%part%2%to%confirm%the%quadruple%angle%
4 tan x − 4 tan 3 x
formula,%that% tan ( 4x ) =
.%Hint:% tan ( 4x ) = tan ( 3x + x ) %%
1− 6 tan 2 x + tan 4 x
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The%tangent%angle%addition%formula%states%that% tan ( a + b ) =