What do you get when $[tan(x)]^2$ ? Is it $tan^2(x)$ or $tan(x)^2$ ? Also is $tan(tan(x))$ same as $tan^2(x)$ ?

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Answer 1 · 2017-12-27T10:16:26

$(tan(x))^2 = tan^2 x$

Expressions like $sin^2 x$ , $cos^2 x$ and $tan^2 x$ are really shorthand for $(sin(x))^2$ , $(cos(x))^2$ and $(tan(x))^2$ respectively.

Note that if conventions are not clear, then when we write $tan x^2$ we could intend $tan(x^2)$ or $(tan(x))^2$ .

So the popular practice is to write $tan^2 x$ when we mean $(tan(x))^2$ and $tan(x^2)$ when we mean $tan(x^2)$ .

It certainly saves on parentheses, but gets a little confusing when you meet $tan^(-1) x$ , which is not $(tan x)^(-1)$ but the inverse tangent.

Note that $tan(tan(x))$ is not the same as $tan^2(x)$ .

What do you get when [tan(x)]^2[tan(x)]^2? Is it tan^2(x)tan^2(x) or tan(x)^2tan(x)^2? Also is tan(tan(x))tan(tan(x)) same as tan^2(x)tan^2(x)?