Where is the mistake in my solution? Trigonometry proof 
To prove: $$1 + 2 \sin 70^\circ = \frac{1}{2\sin 20^\circ}$$

My attempt:
$$\begin{align}
1 + 2 \sin 70^\circ &= 1 + \frac{\sin 140^\circ}{\cos 70^\circ} \\[6pt]
&= 1 + \frac{\sin 40^\circ}{\sin 20^\circ} \\[6pt]
&= \frac{\sin 20^\circ + \sin 40^\circ}{\sin 20^\circ} \\[6pt]
&= \frac{2\sin 30^\circ \cos 10^\circ}{\sin 20^\circ} \\[6pt]
&= \frac{\cos 10^\circ}{2\sin 10^\circ \cos 10^\circ} \\[6pt]
&= \frac{1}{2\sin 10^\circ} \\
\end{align}$$
Can anyone explain where my mistake is?
(original solution image)

As noted in the comments:


*

*The original identity is wrong (LHS $\approx 2.88$, RHS $\approx 1.46$).

*Your derivation of $1 + 2 \sin 70^\circ =  \dfrac{1}{2\sin 10^\circ}$is correct.

