zasady trygonometrii

[logs4]

uzywajac zasady cos(A+B) udowodnij ze\(\displaystyle{ cos =1-2sin^{2}( \frac{1}{2} )}\)

[meninio]

\(\displaystyle{ \cos x=\cos ft(\frac{x}{2}+\frac{x}{2} \right) =\cos \frac{x}{2} \cos \frac{x}{2}-\sin \frac{x}{2} \sin \frac{x}{2} =\cos^2 \frac{x}{2}-\sin^2 \frac{x}{2} =1-\sin^2 \frac{x}{2}-\sin^2 \frac{x}{2}=1-2\sin^2 \frac{x}{2}}\)