Answer
Please refer to the step-by-step part below to see the detailed solution.
Work Step by Step
RECALL:
(1) $\sec{\theta} = \dfrac{1}{\cos{\theta}}$
(2) $1 - \cos^2{\theta}=\sin^2{\theta}$
Use rule (1) above to obtain:
$\sec{\theta} - \cos{\theta} = \dfrac{1}{\cos{\theta}}-\cos{\theta}$
Make the terms similar using their LCD of $\cos{\theta}$ to obtain:
$\dfrac{1}{\cos{\theta}} - \cos{\theta}
\\= \dfrac{1}{\cos{\theta}}-\dfrac{\cos{\theta} \cdot \cos{\theta}}{\cos{\theta}}
\\=\dfrac{1}{\cos{\theta}} - \dfrac{\cos^2{\theta}}{\cos{\theta}}$
Subtract the numerators and copy the denominator to obtain:
$=\dfrac{1-\cos^2{\theta}}{\cos{\theta}}$
Use rule (2) above to obtain:
$\dfrac{1-\cos^2{\theta}}{\cos{\theta}}=\dfrac{\sin^2{\theta}}{\cos{\theta}}$
Thus, the left side of the equation is equal to the right side of the equation.
The statement is true.
