Find \(\displaystyle{\frac{{{\tan{{54}}}-{\tan{{2}}}}}{{{\frac{{{\sin{{2}}}}}{{{\cos{{6}}}}}}+{\frac{{{\sin{{6}}}}}{{{\cos{{18}}}}}}+{\frac{{{\sin{{18}}}}}{{{\cos{{54}}}}}}}}}\)

Aiyana Ayers

Aiyana Ayers

Answered question

2022-04-12

Find tan54tan2sin2cos6+sin6cos18+sin18cos54

Answer & Explanation

shanna87mn

shanna87mn

Beginner2022-04-13Added 19 answers

sinxcos3x=sin3x-x2cosxcos3x=?
and now we have
sinxcos3x=12sin3x-xcosxcos3x=sin3xcosx-sinxcos3x2cosxcos3x=12tan3x-12tanx
so
sin2cos6+sin6cos18+sin18cos54=12tan6-12tan2+12tan18-12tan6+12tan54-12tan18
=12(tan54-tan2)
hence
S=tan54-tan212(tan54-tan2)=2

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