Trigonometric functions (both geometric and circular), relationships between lengths and angles in triangles, and other topics relating to measuring triangles.

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Formula for cos(k*x)

I need to proof that \begin{align} c_k =&\; \cos(k\!\cdot\!x)\\ c_k =&\; c_{k-1} +d_{k-1}\\ d_k :=&\; 2d_0\!\cdot\!c_k +d_{k−1}\\ d_0 :=&\; −2\!\cdot\!\sin^2{(x/2)}\\ \end{align} I ...