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)#?

1 Answer
Dec 27, 2017

#(tan(x))^2 = tan^2 x#

Explanation:

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)#.