Question

Упростить :
Cos 72 + cos 18

Answer 1

$\cos72^o+cos18^0=\cos\left(90^0-18^o\right)+\cos\left(0^0+18^0\right)=\\ =\cos90^0\cdot\cos18^0+\sin90^0\cdot\sin18^0+\cos0^0\cdot\cos18^0-sin0^0\cdot\sin18^0=\\ =0\cdot\cos18^0+1\cdot\sin18^0+1\cdot\cos18^0-0\cdot\sin18^0=\\ =sin18^0+\cos18^0$