Hey, I'm just like... completely zoned out:
sin x = cos ( 2x + 15 )
This is incorrect. For example, let $\displaystyle x = \frac{\pi}2$. The actual identity should be $\displaystyle \sin x = \cos\left(\frac{\pi}2 - x\right)$. Then we have:
$\displaystyle \cos\left(\frac{\pi}2 - x\right) = \cos(2x + 15)$
Note, however, that there will be infinitely many solutions due to the periodicity of the cosine.
And Kuczaj, did you even try your answer? I get
$\displaystyle \begin{array}{rcr@{.}l}
\sin 25^\circ & \approx & 0&42261826174\\
\cos\left(2\left(25^\circ\right) + 15\right) & \approx & -0&986467363994
\end{array}$