How do you evaluate tan1(tan(7π6))?

1 Answer
Jul 24, 2016

7π6

Explanation:

When the operation is "inverse of a function over the function# on

an operand 'a', the result is 'a'.

Symbolically., f1f(a)=a.

Here, f=tan,f1=tan1 and the operand a=7π6

So, the answer is 7π6

The conventional restriction on

'a' as the principal value [π2,π2]

has no relevance for this double operation.

If the question is about tan1tan(π6),

the value will be (π6).

In either case the tan value = 13..

Of course, the principal value of tan1(13)=π6

The source for the value 7π6 is the general value

nπ+π6,n=1.. . .

..