Use a graphing calculator to make a conjecture as to whether each equation is an identity.
-$$\frac { \cos ^ { 2 } x } { \sin ^ { 2 } x } + \cos x \sec x$$
A) $\csc x$
B) $\csc ^ { 2 } x$
C) $\sec ^ { 2 } x$
D) $\cot ^ { 2 } x$

Question

Quizplus · Accepted Answer

The given equation simplifies to $\csc^2 x$. The first term $\frac{\cos^2 x}{\sin^2 x}$ simplifies to $\cot^2 x$, and the second term $\cos x \sec x$ simplifies to $1$ because $\sec x = \frac{1}{\cos x}$. Therefore, the equation becomes $\cot^2 x + 1$, which is equal to $\csc^2 x$ according to the Pythagorean identity.

Use a Graphing Calculator to Make a Conjecture as to Whether