Question1. a. Express $\cos (x)$ in terms of $\cot (x)$ and $\csc (x)$. b. Express $\csc (x)$ in terms of $\cos (x)$ and $\tan (x)$.

Studdy Solution
Express $\sin(x)$ in terms of $\cos(x)$ and $\tan(x)$:
Rearrange the expression for $\tan(x)$:
$\sin(x) = \tan(x) \cdot \cos(x)$
Since $\csc(x) = \frac{1}{\sin(x)}$, substitute the expression for $\sin(x)$:
$\csc(x) = \frac{1}{\tan(x) \cdot \cos(x)}$
Thus, $\csc(x) = \frac{1}{\tan(x) \cdot \cos(x)}$.
The expressions are: a. $\cos(x) = \frac{\cot(x)}{\csc(x)}$ b. $\csc(x) = \frac{1}{\tan(x) \cdot \cos(x)}$