Answer
Given $cos \theta = \frac{1}{sec\theta}$, two equivalent forms of this identity are $sec \theta = \frac{1}{cos \theta}$ and $cos\theta * sec\theta = 1$.
Work Step by Step
To get the equivalent forms of the identity, we just need to solve it for the two other values in the identity.
Solving for $sec\theta$.
With cross multiplication, we get
$sec\theta = \frac{1}{cos\theta}$
Solving for 1,
Multiplying both sides by $\sec\theta$. we get
$\cos\theta\ * \sec\theta = \frac{1}{\sec\theta} * \sec\theta$
Since $\frac{\sec\theta}{\sec\theta} = 1$ this gives us the answer:
$\cos\theta\ * \sec\theta = {1}$
Therefore given $cos \theta = \frac{1}{sec\theta}$, two equivalent forms of this identity are $sec \theta = \frac{1}{cos \theta}$ and $cos\theta * sec\theta = 1$.
