How do you evaluate $\tan \left[ {\arccos \left( {\dfrac{1}{3}} \right)} \right]$?

Hint:“$\arccos $” is nothing but a inverse of $\cos \theta $, to solve this problem first evaluate the term which is present inside the bracket and then multiply it with the answer which is present inside the bracket.

Complete step by step solution:
Let us consider the problem,
$\tan \left[ {\arccos \left( {\dfrac{1}{3}} \right)} \right]$ … (1)

Here, let’s consider the bracketed term $\arccos \left( {\dfrac{1}{3}} \right)$ and let us solve this first we get,

$\arccos \left( {\dfrac{1}{3}} \right)$$ = \arccos (0.3333) = 70.53$

Solving the bracketed term, we got $70.53$, Substituting the value in the (1) equation we get,
$\tan \left[ {70.53} \right] = 2.8286$

This is our required solution.

Additional information: Solve $\left[ {\left( {2*\dfrac{6}{3}} \right) + 24*26 - 9} \right]$, be careful while solving these types of problems.

Use the BODMAS rule here, first consider the number which is inside the bracket. The number is $\left( {2*\dfrac{6}{3}} \right)$, by solving we get 4, Then multiply $24*26$ which is equal to $624$.

Now the given question becomes $4 + 624 - 9 = 619$, This is our required solution. First, we solved the numbers which is the bracketed term and then we performed division. After that we multiplied the two numbers which are present outside the bracket and at last, we performed the addition and subtraction. This is the way to simplify a problem.

Note: BODMAS rule is a rule in which we have to simplify the question. In BODMAS, B stands for bracket, O stands for orders of, D stands for division, M stands for multiplication, A stands for addition and S stands for subtraction.

 If a problem has lots of bracketed term multiplication, division, addition and subtraction, then don’t forget to use this rule in the same order, this rule is to remind you the order in which you have to solve some complicated problems.