Question

Determine o valor de sen 75- cos75

Answer 1

sen75°=sen(135°-60°)

sen(135°-60°)=sen135°.cos60°- sen60°.cos135°

sen(135°-60°)=√2/2.1/2-√3/2.(-√2/2)

sen 75°=√2/4+√2.√3/4

sen 75°=2√2.√3/4

sen 75°= √2.√3/2

cos(135°-60°)=cos135°.cos60°+sen135°.sen60°

cos 75°= -√2/2.1/2+√2/2.√3/2

cos 75°= -√2/4+√2.√3/4

cos 75°= 2√2.√3/4

cos 75°=√2.√3/2

sen75°-cos75°=

√2.√3/2-√2.√3/2=0