Question

1. Explain the mechanism and reason of the first method?

2.: Explain the 2nd method ans (alternative)

Answer 1

1. It is a standard method of solving questions like { If x+(1/x)=n, find {x^2 + (1/x^2)} }.

If you square both sides, you will get the answer easily. This is what it has done there to get the answer.

2. In the alternative, it has just solved the equation.

You are given tan x + (1/ tan x) = 2. Now solve the equation.

$\tan(x) + \frac{1}{ \tan(x) } = 2 \\ \\ \Rightarrow \frac{ { \tan }^{2}x + 1 }{ \tan(x) } = 2$

$\Rightarrow { \tan }^{2} x + 1 = 2 \tan(x)$

I think you can see from the book what is to be done after that.