опростете тъждествата ;/

[noobnoob234]

[t1bld]

[tex](sin\alpha + sin\beta )^2 + (cos\alpha +cos\beta )^2=sin^2\alpha +cos^2\alpha +sin^2\beta +cos^2\beta + 2sin\alpha sin\beta + 2cos\alpha cos\beta =2 + 2(sin\alpha sin\beta +cos\alpha cos\beta )=2 + 2cos(\alpha -\beta )[/tex]

[t1bld]

[tex]1 - 2cos\alpha + cos2\alpha =1 - 2cos\alpha +cos^2\alpha - sin^2\alpha =2 cos^2\alpha - 2 cos\alpha =2cos\alpha (cos\alpha - 1)[/tex]

[t1bld]

[tex]4cos^2\alpha - 3=2 + 2cos2\alpha - 3=2cos2\alpha - 1=cos^2\alpha -3sin^2\alpha=(cos\alpha - \sqrt{3} sin\alpha )(cos\alpha + \sqrt{3}sin\alpha )[/tex]

[t1bld]

[tex]sin4\alpha /(1+ cos4\alpha)*cos2\alpha/(1+cos2\alpha )*cos\alpha/(1 + cos\alpha ) sin4\alpha /2cos^2(2\alpha )*cos2\alpha /2cos^2 \alpha*cos\alpha /(1+cos\alpha )=1/4 sin4\alpha/(1+cos\alpha ) =1/2 sin^2(2\alpha )cos^2(2\alpha) /(1+cos\alpha)=1/2 (1-cos^4\alpha)/(1+cos\alpha)=1/2 (1-cos\alpha )(1+cos^2\alpha )[/tex]