Question

Is cot inverse of tan?

Answer 1

Hint : Using the $tan^-1$ convention may lead to confusion about the difference between arctangent and cotangent. It turns out that arctan and cot are really separate things:

Complete step-by-step answer :
There is a huge difference between the inverse and reciprocal of the trigonometric value.
Reciprocal is nothing but the reverse of the $\dfrac{p}{q}$ form of the trigonometric equation. And inverse is the inverse functions of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant functions. They are also termed as arcus functions, anti trigonometric functions or cyclometric functions. These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios.
$\cot (x) = \dfrac{1}{{\tan (x)}}$ , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse
arctan(x) is the angle whose tangent is x

Note : We hope that now you do not doubt that arctan and cotan are different. To avoid any further misunderstandings, you may want to use the arctan(x) rather than $tan^-1$ notation.
Most people think that cot is the inverse of tan but it is not. We hope that now you do not doubt that arctan and cotan are different. To avoid any further misunderstandings, you may want to use the arctan(x) rather than $tan^-1$ notation.