How to simplify tan(-x)cos(-x)?

Kayley Kidd

Kayley Kidd

Answered question

2023-01-08

How to simplify tan(x)cos(x)?

Answer & Explanation

Ioriannis4v

Ioriannis4v

Beginner2023-01-09Added 11 answers

tan(x)cos(x)
=sin(x)cos(x)cos(x)
=sin(x)
sinx
Destiney Barrett

Destiney Barrett

Beginner2023-01-10Added 4 answers

\(\displaystyle{\color{\quad\textor\quadan\ge}\text{}}{R}{e}\min{d}{e}{r}{s}\text{}\)
\(\displaystyle{\color{red}{{\mid}\overline{{\underline{{{\color{white}{\frac{{a}}{{a}}}}{\color{black}{{\tan{{x}}}=\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}}}{\color{white}{\frac{{a}}{{a}}}}{\mid}}}}}}}{\quad\text{and}\quad}{\color{red}{{\mid}\overline{{\underline{{{\color{white}{\frac{{a}}{{a}}}}{\color{black}{{\sin{{\left(-{x}\right)}}}=-{\sin{{x}}}}}{\color{white}{\frac{{a}}{{a}}}}{\mid}}}}}}}\)
\(\displaystyle\Rightarrow{\tan{{\left(-{x}\right)}}}{\cos{{\left(-{x}\right)}}}=\frac{{{\sin{{\left(-{x}\right)}}}}}{{\cancel{{{\cos{{\left(-{x}\right)}}}}}}}\times\cancel{{{\cos{{\left(-{x}\right)}}}}}\)
\(\displaystyle={\sin{{\left(-{x}\right)}}}=-{\sin{{x}}}\)

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