How do I slove this AND where am I making the mistake?

[left merlin]

Slove 🥀

[hearty sigil]

You make the mistake at the first

$(a/(a+1) + (a+1)/a)

[crisp hull]

Yeah I realized the mistake after I posted😭
Simplify*

[crisp hull]

I don't think I understand that

[eternal frigate]

$$
\frac{\rom{tg}^2 x}{1+\rom{tg}^2 x} + \frac{1 + \rom{tg}^2 x}{\rom{tg}^2 x}
$$

[sick cradle]

tota nox

[eternal frigate]

that what you mean?

,align
\frac{\rom{tg}^2 x}{1+\rom{tg}^2 x} + \frac{1 + \rom{tg}^2 x}{\rom{tg}^2 x} &= \frac{\rom{tg}^4 x + \left( 1 + \rom{tg}^2 x \right)^2}{\left(\rom{tg}^2 x \right)\left(1 + \rom{tg}^2\right)} \
&= \frac{1 + 2\rom{tg}^2 + 2\rom{tg}^4 x}{\rom{tg}^2 x + \rom{tg}^4 x}

[sick cradle]

tota nox

[eternal frigate]

ok wait

$\frac{\rom{tg}^2 x}{1 + \rom{tg}^2 x} = \sin^2 x$

[sick cradle]

tota nox

[eternal frigate]

so this is just $\sin^2 x + \csc^2 x$

[sick cradle]

tota nox

[crisp hull]

Nope, it's
tg²x/(1+tg²x) + (1+ctg²x)/ctg²x