Question

Which of the following is the expansion of tan x?

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is E

This is one of the expansion we have given you in the beginning of topic.

It is better to remember the expansion.

The derivation of some of these series is difficult. Sin x and cos x can be derived as

$sinx=\frac{e^{ix}-e^{-ix}}{2i}$

and $cosx=\frac{e^{ix}+e^{-ix}}{2}$

For this we need to know the expansion of $e^x$. We won't discuss derivation of tanx.

In our question, we can find it by eliminating the option.

For x=0, tan x should be zero. Only A and E satisfy this.

We can also see that for $x=\frac{\pi }{2}$, Option 'A' won't tend to infinity or

those who know the expansion of sin x. option A can be eliminated.

So 'E' is the correct answer.

$\Rightarrow tanx=x+\frac{x^3}{3}+\frac{2x^5}{15}....$