Pembuktian Trigonometri : Soal dan Pembahasan

Berikut ini adalah kumpulan soal mengenai pembuktian trigonometri. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.

1. Buktikan identitas trigonometri berikut.
   \cos^4\alpha=\dfrac38+\dfrac12\cos\alpha+\dfrac18\cos4\alpha
   
   $\begin{array}{rl}{\cos }^4\alpha & ={({\cos }^2\alpha )}^2\\ & ={({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\cos 2\alpha )}^2\\ & ={\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{2}}\cos \alpha +{\displaystyle \frac{1}{4}}{\cos }^{2}2\alpha \\ & ={\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{2}}\cos \alpha +{\displaystyle \frac{1}{4}}({\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\cos 4\alpha )\\ & ={\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{2}}\cos \alpha +{\displaystyle \frac{1}{8}}+{\displaystyle \frac{1}{8}}\cos 4\alpha \\ & ={\displaystyle \frac{3}{8}}+{\displaystyle \frac{1}{2}}\cos \alpha +{\displaystyle \frac{1}{8}}\cos 4\alpha \end{array}$

   Jadi,
   
   
2.