Question

How do you use trigonometric identities to transform one side of the equation into the other $\cos \theta sec\theta =1$?

Answer 1

Transforming one side of the equation into the other.

The given equation is $\cos \theta \sec \theta =1$.

The multiplicative inverse of $\sec \theta$ is given by,

$\sec \theta =\frac{1}{\cos \theta }...\left(1\right)$

Now, putting the value of $\sec \theta$ in the $\text{LHS}$ of the given equation:

$\begin{array}{rcl}\mathrm{LHS}& =& \cos \theta \times \sec \theta \\ & =& \cos \theta \times \frac{1}{\cos \theta }[Fromequation(1\left)\right]\\ & =& 1\\ \therefore \text{LHS}& =& \mathrm{RHS}\end{array}$

Hence, $\cos \theta \sec \theta =1$.