Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.
-$$\frac { 4 + 7 \tan x } { \sin x } = 4 \csc x + 7 \sec x$$
A) Identity
B) Not an Identity

Question

Quizplus · Accepted Answer

The given equation can be simplified using trigonometric identities. Recall that $\csc x = \frac{1}{\sin x}$ and $\sec x = \frac{1}{\cos x}$. Also, $\tan x = \frac{\sin x}{\cos x}$. Substituting these into the equation, we get $\frac{4\sin x + 7\sin x / \cos x}{\sin x} = 4 \cdot \frac{1}{\sin x} + 7 \cdot \frac{1}{\cos x}$. Simplifying both sides gives the same expression, confirming the equation is an identity.

Graph the Expression on Each Side of the Equals Symbol 4+7tan⁡xsin⁡x=4csc⁡x+7sec⁡x\frac { 4 + 7 \tan x } { \sin x } = 4 \csc x + 7 \sec xsinx4+7tanx​=4cscx+7secx

Graph the Expression on Each Side of the Equals Symbol $\frac { 4 + 7 \tan x } { \sin x } = 4 \csc x + 7 \sec x$