tell whether the statement is true or false. if false, tell why. the graph of y = tan x in the figure to the…

tell whether the statement is true or false. if false, tell why. the graph of y = tan x in the figure to the right suggests that tan( - x)=tan x for all x in the domain of tan x. choose the correct answer below. a. true b. false; tan( - x)= - tan x for all x in the domain. c. false; there is no relation between tan( - x) and tan x.
Answer
Explanation:
Step1: Recall tangent - function property
The tangent function (y = \tan x=\frac{\sin x}{\cos x}). And (\sin(-x)=-\sin x), (\cos(-x)=\cos x). Then (\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\tan x).
Step2: Analyze the given statement
The statement (\tan(-x)=\tan x) for all (x) in the domain of (\tan x) is false because of the odd - function property of the tangent function.
Answer:
B. False; (\tan(-x)=-\tan x) for all (x) in the domain.