Question

What basic trigonometric identity would you use to verify that

Answer 1

Given the equation:

$\frac{\sin^2x+\text{cos}^2x}{\cos x}=\sec x$

Let's determine the trigonometric identity that you could be used to verify the exquation.

Let's determine the identity:

Apply the trigonometric identity:

$\sin ^2x+\cos ^2x=1$

$\cos x=\frac{1}{\sec x}$

Replace cosx for 1/secx

Thus, we have:

$\begin{gathered} \frac{\sin^2x+\cos^2x}{\frac{1}{\sec x}} \\ \\ =(\sin ^2x+\cos ^2x)(\sec x) \\ \text{Where:} \\ (\sin ^2x+\cos ^2x)=1 \\ \\ We\text{ have:} \\ (\sin ^2x+\cos ^2x)(\sec x)=1\sec x=\sec x \end{gathered}$

The equation is an identity.

Therefore, the trignonometric identity you would use to verify the equation is:

$\cos ^2x+\sin ^2x=1$

ANSWER:

$\cos ^2x+\sin ^2x=1$