Is this correct: tan^-2 x = (tan x)^-2 but tan^-1 x != (tan x)^-1
.......
= tan^-2 x = cotan^2 x and tan^-1 x = atan x
.......
I find this very confusing?
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d/dx (cosec x) = d/dx (sin^-1 x) is incorrect notation?
while d/dx (cosec^2 x) = d/dx (sin^-2 x) is correct notation?

Question

Is this correct: tan^-2 x = (tan x)^-2 but tan^-1 x != (tan x)^-1
.......
=> tan^-2 x = cotan^2 x and tan^-1 x = atan x
.......
I find this very confusing?
.......
d/dx (cosec x) = d/dx (sin^-1 x) is incorrect notation?
while d/dx (cosec^2 x) = d/dx (sin^-2 x) is correct notation?

anonymous · Answer

Honestly , I don't like this notation : tan^-1...arctan is much better and less confusing ! 
tan^-1 is the inverse of "tan" ( restricted to ]-pi/2;pi/2[)...not 1/tan....tan^2 or tan^2 can be accpted...but tan^-2...I don't think soo...!!

stacey · Answer

The -1 exponent is used to express arctan or arcsin. For this reason we usually do not use negative exponents like -2 on the trig functions. We usually will write it as a fraction.

l8fish · Answer

Ok thanks for the responses.