Question

Calcule sen 15 + cos 15

Answer 1

Resposta:

sen(a-b)=sen(a)*cos(b) - sen(b)*cos(a)

cos(a-b)=cos(a)*cos(b) + sen(a)*sen(b)

sen(45-30) =sen(45)*cos(30) - cos(45)*sen(30)

sen(15)=√2/2 * √3/2 -√2/2* 1/2

cos(45-30) =cos(45)*cos(30) + sen(45)*sen(30)

cos(15) =√2/2 *√3/2 +√2/2*1/2

sen 15 + cos 15 =  √2/2 * √3/2 -√2/2* 1/2 +√2/2 * √3/2 +√2/2* 1/2

sen 15 + cos 15 =  √2/2 * √3/2  +√2/2 * √3/2

sen 15 + cos 15 =  √2 * √3/2  = √6/2