Question

sen 75° cos 38° - cos 75° sen 38°

Answer 1

Estamos en presencia del seno de una diferencia.

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

sen(75°-38°)=sen75°cos38°-cos75°sen38°

Sabemos que el sen75° va a ser igual a sen(45°+30°)

sen(45°+30°)= sen(45°+30°)=sen(45)cos(30)+cos(45)sen(30)

sen75°=√2/2*√3/2+√2/2*1/2=√6/4+√2/4

sen75°=√6+√2/4

cos75°=cos(30°+45°)=cos30°*cos45°-sen30°sen45°

cos75°=√3/2*√2/2-1/2*√2/2

cos75°=√6/4-√2/4

cos75°=√6-√2/4

Entonces,

sen75°=0.966

cos75°=0.259

sen38°=0.616

cos38°=0.788

sen(75°-38°)=(0.966*0.788)-(0.259*0.616)

sen(75°-38°)=0.178-(-0.357)

sen(75°-38°)=0.535°