Question

Докажите тождество:sin(a-β)-cos a sin(-β)=sin a cos βВычислите:соs18° cos63°+sin18° sin63°

Answer 1

Вычислите:

соs18° cos63°+sin18° sin63° =  cos63°соs18°+sin63° sin18° = cos (63°-18°)= cos 45° =√2/2

 

Answer 2

$sin(\alpha -\beta)-cos\alpha sin(-\beta)=(sin\alpha cos\beta-cos\alpha sin\beta)-\\ -cos\alpha (-sin\beta)=sin\alpha cos\beta$

 

cos18cos63+sin18sin63=cos(18-63)=cos(-45)=cos(45)=$\frac{1}{\sqrt2}$