How to simplify the expression sec^2x-1?

Kadyn Acevedo

Kadyn Acevedo

Answered question

2023-01-16

How to simplify the expression sec2x−1?

Answer & Explanation

CredyBetCreta109

CredyBetCreta109

Beginner2023-01-17Added 11 answers

Using the \(\displaystyle{\color{blue}\text{}}{t}{r}{i}{g}{o}{n}{o}{m}{e}{t}{r}{i}{c}{i}{d}{e}{n}{t}{i}{t}{y}\text{}\)
\(\displaystyle{\color{red}{\overline{{\underline{{{\left|{\color{white}{\frac{{a}}{{a}}}}{\color{black}{{{\sin}^{{2}}{x}}+{{\cos}^{{2}}{x}}={1}}}{\color{white}{\frac{{a}}{{a}}}}\right|}}}}}}}\)
divide all terms on both sides by \(\displaystyle{{\cos}^{{2}}{x}}\)
\(\displaystyle\Rightarrow\frac{{{{\sin}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}+\frac{{{{\cos}^{{2}}{x}}}}{{{{\cos}^{{2}}{x}}}}=\frac{{1}}{{{{\cos}^{{2}}{x}}}}\)
\(\displaystyle{\color{\quad\textor\quadan\ge}\text{}}{R}{e}\min{d}{e}{r}\text{}\)
\(\displaystyle{\color{red}{\overline{{\underline{{{\left|{\color{white}{\frac{{a}}{{a}}}}{\color{black}{{\tan{{x}}}=\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}\text{}{\quad\text{and}\quad}\text{}{\sec{{x}}}=\frac{{1}}{{{\cos{{x}}}}}}}{\color{white}{\frac{{a}}{{a}}}}\right|}}}}}}}\)
\(\displaystyle\Rightarrow{{\tan}^{{2}}{x}}+{1}={{\sec}^{{2}}{x}}\)
Take 1 away from both sides.
\(\displaystyle{{\tan}^{{2}}{x}}\cancel{{+{1}}}\cancel{{-{1}}}={{\sec}^{{2}}{x}}-{1}\)
\(\displaystyle\Rightarrow{{\sec}^{{2}}{x}}-{1}={{\tan}^{{2}}{x}}\)
y1i2de1o64w

y1i2de1o64w

Beginner2023-01-18Added 2 answers

super!

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