tan^2(x) + 1 = sec^2(x) Archives - Epsilonify Best solutions on internet! Thu, 14 Sep 2023 21:36:11 +0000 en-US hourly 1 https://wordpress.org/?v=6.4.5 https://www.epsilonify.com/wp-content/uploads/2022/09/cropped-E-M7-32x32.png tan^2(x) + 1 = sec^2(x) Archives - Epsilonify 32 32 Prove that tan^2(x) + 1 = sec^2(x) https://www.epsilonify.com/mathematics/calculus/prove-that-tan-square-x-plus-1-is-equal-to-sec-square-x/ https://www.epsilonify.com/mathematics/calculus/prove-that-tan-square-x-plus-1-is-equal-to-sec-square-x/#respond Mon, 16 Jan 2023 13:00:53 +0000 https://www.epsilonify.com/?p=1879 The function is equal to . Proof. We have seen here that: Now multiply both sides with gives us: We do know that and . Therefore, we get the following: Therefore, is equal to .

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]]> \tan^2(x) + 1 is equal to \sec^2(x).

Proof. We have seen here that: 
\begin{align*}
\sin^2(x) + \cos^2(x) = 1.
\end{align*}
Now multiply both sides with \frac{1}{\cos^2(x)} gives us: 
\begin{align*}
\frac{\sin^2(x)}{\cos^2(x)} + 1 = \frac{1}{\cos^2(x)}.
\end{align*}
We do know that \frac{\sin^2(x)}{\cos^2(x)} = \tan^2(x) and \frac{1}{\cos^2(x)} = \sec^2(x). Therefore, we get the following: 
\begin{align*}
\tan^2(x) + 1 = \sec^2(x).
\end{align*}
Therefore, \tan^2(x) + 1 is equal to \sec^2(x).

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