Solved example of Quotient of powers

Take $\frac{\pi }{2}$ out of the fraction

The limit of a sum of two functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

Multiplying polynomials $\tan\left(\sqrt{2}x\right)$ and $\lim_{x\to1}\left(x\right)+\lim_{x\to1}\left(-1\right)$

The limit of a constant is just the constant

Evaluating the limit when $x$ tends to $1$

Simplifying

Subtracting $\tan\left(\sqrt{2}x\right)$ and $\tan\left(\sqrt{2}x\right)$