Question

How do you find the value for \[\tan \left[ {{{\tan }^{ - 1}}\left( {7.4} \right)} \right]\] ?

Answer 1

Hint: Given is a trigonometric function depending question. We have to find the value using an inverse trigonometric function. Inverse trigonometric function can be \[\tan \left[ {{{\tan }^{ - 1}}\theta } \right]\] or \[{\tan ^{ - 1}}\left[ {\tan \theta } \right]\]. These are patterned differently but are having the same result. So we will use this inverse function identity.

Complete step-by-step answer:
Given is \[\tan \left[ {{{\tan }^{ - 1}}\left( {7.4} \right)} \right]\]
We know that \[\tan \left[ {{{\tan }^{ - 1}}\theta } \right] = \theta \]
Thus just comparing given function with the general function we get,
\[\theta = 7.4\]
This is the correct answer.
So, the correct answer is “7.4”.

Note: Note that this question is very easy to solve only when we know the inverse identity has the result as the angle itself.
Like tan function all other functions have the same result. Like \[\sin \left[ {{{\sin }^{ - 1}}\theta } \right] = \theta \] all remaining trigonometric identity. We just have to replace the inverses of the respective functions. Note that inverse and reciprocal are two different concepts. They are not the same in case of these problems of trigonometry.
If the question has options in which the angle is in degrees and of same value in radians, then both are correct.