Question
Write each expression in terms of sines and or cosines and then simplify secx and cosx
Answers
Answered by
GPT 3.5
In order to express each expression in terms of sines and/or cosines, we can use the following trigonometric identities:
1. $\sec(x) = \frac{1}{\cos(x)}$
2. $\cos(x) = \sqrt{1 - \sin^2(x)}$
Using these identities, we can simplify $\sec(x)$ and $\cos(x)$ as follows:
1. $\sec(x) = \frac{1}{\cos(x)}$
2. $\cos(x) = \sqrt{1 - \sin^2(x)}$
For example, if we were given an expression like $\sec^2(x)$, we could rewrite it as $\left(\frac{1}{\cos(x)}\right)^2$.
Similarly, if we were given an expression like $\frac{1}{\cos^2(x)}$, we could rewrite it as $\frac{1}{\left(\sqrt{1 - \sin^2(x)}\right)^2}$.
To fully simplify each expression, we would need to know the specific expressions given.
1. $\sec(x) = \frac{1}{\cos(x)}$
2. $\cos(x) = \sqrt{1 - \sin^2(x)}$
Using these identities, we can simplify $\sec(x)$ and $\cos(x)$ as follows:
1. $\sec(x) = \frac{1}{\cos(x)}$
2. $\cos(x) = \sqrt{1 - \sin^2(x)}$
For example, if we were given an expression like $\sec^2(x)$, we could rewrite it as $\left(\frac{1}{\cos(x)}\right)^2$.
Similarly, if we were given an expression like $\frac{1}{\cos^2(x)}$, we could rewrite it as $\frac{1}{\left(\sqrt{1 - \sin^2(x)}\right)^2}$.
To fully simplify each expression, we would need to know the specific expressions given.