Question

Determine the exact value of expression. tan(330)timescos(240)-2cos(270)

Trigonometry
ANSWERED
asked 2021-02-05
Determine the exact value of expression.
\(\displaystyle{\tan{{\left({330}\right)}}}\times{\cos{{\left({240}\right)}}}-{2}{\cos{{\left({270}\right)}}}\)

Answers (1)

2021-02-06
Given,
\(\displaystyle{\tan{{\left({330}\right)}}}\times{\cos{{\left({240}\right)}}}-{2}{\cos{{\left({270}\right)}}}\)
Now,
\(\displaystyle{\tan{{\left({330}\right)}}}\times{\cos{{\left({240}\right)}}}-{2}{\cos{{\left({270}\right)}}}\)
\(\displaystyle={\tan{{\left({360}-{30}\right)}}}\times{\cos{{\left({180}+{60}\right)}}}-{2}{\cos{{\left({270}\right)}}}\)
\(\displaystyle=-{\tan{{\left({30}\right)}}}\times{\left(-{\cos{{\left({60}\right)}}}\right)}-{2}{\left({0}\right)}\)
\(\displaystyle=-{\frac{{{1}}}{{\sqrt{{{3}}}}}}\times{\left(-{\frac{{{1}}}{{{2}}}}\right)}\)
\(\displaystyle={\frac{{{1}}}{{{2}\sqrt{{{3}}}}}}\)
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