Diketahui:

$\sin\left(x+15\degree\right)=\cos\left(2x+54\degree\right)$

Ditanya:

$x=?$

Jawab:

Perhatikan relasi sudut di bawah ini.

Berdasarkan gambar di atas diperoleh,

$\sin\left(90\degree-\alpha\right)=\cos\alpha$, maka

$\cos\left(2x+54\degree\right)=\sin\left(90\degree-\left(2x+54\degree\right)\right)$

sehingga

$\sin\left(x+15\degree\right)=\cos\left(2x+54\degree\right)$

$\Leftrightarrow\sin\left(x+15\degree\right)=\sin\left(90\degree-\left(2x+54\degree\right)\right)$

$\Leftrightarrow\sin\left(x+15\degree\right)=\sin\left(90\degree-2x-54\degree\right)$

$\Leftrightarrow\sin\left(x+15\degree\right)=\sin\left(36\degree-2x\right)$

$\Leftrightarrow\left(x+15\degree\right)=\left(36\degree-2x\right)$

$\Leftrightarrow x+2x=36\degree-15\degree$

$\Leftrightarrow3x=21\degree$

$\Leftrightarrow x=\frac{21\degree}{3}$

$\Leftrightarrow x=7\degree$

Jadi, nilai $x$ yang memenuhi adalah $7\degree.$