MathDB

3

Part of 1961 Poland - Second Round

Problems(1)

1-\cos^2x-\cos^2y- y-\cos^2z +2 \cos x \cos y \cos z = ...

Source: Polish MO Second Round 1961 p3

8/31/2024
Prove that for any angles x,y,zx,y,z holds the equality 1−cos⁡2x−cos⁡2y−y−cos⁡2z+2cos⁡xcos⁡ycos⁡z=4sin⁡x+y+z2sin⁡x+y−z2sin⁡x−y+z2sin⁡−x−y+z2.1-\cos^2x-\cos^2y- y-\cos^2z +2 \cos x \cos y \cos z= 4 \sin \frac{x+y+z}{2} \sin \frac{x+y-z}{2} \sin \frac{x-y+z}{2} \sin\frac{-x-y+z}{2}.
trigonometry