Question

Which equation is not an identity?

tan(–t) = –tan t

tan t(csc t + cot t) = sec t + 1

sin tcot t = cos t

cos2t − sin2t = –1

Answer 1

let's look at the first equation
what kinda function is tan?
is it even or odd?

Answer 2

an identity is true for all values of the variable

Answer 3

Well, tangent is an odd function.

Answer 4

I was hoping Alg could tell us that

Answer 5

Okay there are rules,

Identities:
\(\normalsize\color{black}{ \sin(~-t~)=-\sin(~t~) }\)
\(\normalsize\color{black}{ \cos(~-t~)=\cos(~t~) }\)
\(\normalsize\color{black}{ \tan(~-t~)=-\sin(~t~) }\)

Don't confuse:
\(\normalsize\color{red}{ \sin(~-t~) \ne\sin(~t~) }\)
\(\normalsize\color{red}{ \cos(~-t~)\ne -\cos(~t~) }\)
\(\normalsize\color{red}{ \tan(~-t~)=\tan(~t~) }\)

Answer 6

the last one is supposed to be
\(\normalsize\color{red}{ \tan(~-t~) \ne \tan(~t~) }\)