Find out the answer to "How to simplify tan⁡(x)sec⁡(x)?"

High School
Geometry
Trigonometry
Trigonometric equations and identities

Enrique Cunningham

Answered question

2022-12-30

How to simplify

\frac{\tan (x)}{\sec (x)}

Answer & Explanation

Dane Brennan

Beginner2022-12-31Added 9 answers

\frac{\tan x}{\sec x}

= (\tan x) (\cos x)

= \frac{(\sin x) (\cos x)}{\cos x}

= \sin x

Jace Nelson

Beginner2023-01-01Added 4 answers

Using \(\displaystyle{\color{blue}\text{}}{t}{r}{i}{g}{o}{n}{o}{m}{e}{t}{r}{i}{c}{i}{d}{e}{n}{t}{i}{t}{i}{e}{s}\text{}\)
\(\displaystyle{\color{\quad\textor\quadan\ge}\text{}}{R}{e}\min{d}{e}{r}\text{}\)
\(\displaystyle{\color{red}{{\mid}\overline{{\underline{{{\color{white}{\frac{{a}}{{a}}}}{\color{black}{{\tan{{x}}}=\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}\text{}{\quad\text{and}\quad}\text{}{\sec{{x}}}=\frac{{1}}{{{\cos{{x}}}}}}}{\color{white}{\frac{{a}}{{a}}}}{\mid}}}}}}}\)
\(\displaystyle\Rightarrow\frac{{{\tan{{x}}}}}{{{\sec{{x}}}}}=\frac{{\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}}}{{\frac{{1}}{{{\cos{{x}}}}}}}=\frac{{{\sin{{x}}}}}{\cancel{{{\cos{{x}}}}}}\times\frac{\cancel{{{\cos{{x}}}}}}{{1}}={\sin{{x}}}\)

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