vault backup: 2023-04-04 13:19:23

notes/.obsidian/plugins/obsidian-activity-history/data.json

@@ -13,7 +13,7 @@
     {
       "path": "/",
       "date": "2023-04-04",
-      "size": 991266
+      "size": 991493
     }
   ],
   "activityHistory": [
@@ -1158,7 +1158,7 @@
         },
         {
           "date": "2023-04-04",
-          "value": 1941
+          "value": 2168
         }
       ]
     }

notes/.obsidian/plugins/various-complements/data.json

@@ -230,6 +230,14 @@
           "lastUpdated": 1680604049764
         }
       }
+    },
+    "2\\cos\\frac{\\alpha+\\beta}2\\sin\\frac{\\alpha-\\beta}2": {
+      "2\\cos\\frac{\\alpha+\\beta}2\\sin\\frac{\\alpha-\\beta}2": {
+        "currentFile": {
+          "count": 1,
+          "lastUpdated": 1680606991534
+        }
+      }
     }
   }
 }

notes/mat/Funkce/Goniometrické vzorce.md

@@ -29,3 +29,21 @@ $x=k\frac{\pi}3+\frac\pi6$
 $\sin(-2x)=0$
 $-2x=k\pi$
 $x=-k\frac{\pi}2$
+
+---
+
+$\cos x+\cos(3x)=0$
+$\cos\alpha+\cos\beta=2\cos\frac{\alpha+\beta}2\sin\frac{\alpha-\beta}2$
+
+$0=2\cos\frac{x+3x}2\sin\frac{x-3x}2$
+$0=2\cos\frac{4x}2\sin\frac{-2x}2$
+$0=2\cos(2x)\sin(-x)$
+$0=\cos(2x)\sin(-x)$
+
+$\sin(-x)=0$
+$-x=k\pi$
+$x=-k\pi$
+
+$\cos(2x)=0$
+$2x=k\pi+\frac\pi2$
+$x=k\frac\pi2+\frac\pi4$