1. x∈(0,π/2)⇒ sin x>0
cos x>0
sin²x+cos²x=1
(3/5)²+cos²x=1
9/25+cos²x=1
9+25cos²x=25
25cos²x=16
cos²x=16/25
cos x=±√16/25=±4/5
cos x>0 ⇒ cos x=4/5
2. sin 135°=sin(90°+45°)=sin 90°×cos 45°+cos 90°×sin 45°=
=1×√2/2+0×√2/2=√2/2
sin 135°/cos 45°=√2/2/√2/2=1
3. sin 80°=sin(90°-10°)=sin 90°×cos 10°-cos 90°×sin 10°=
=1×cos 10°-0×sin 10°=cos 10°
sin²80°+sin²10°=
=cos²10°+sin²10°=1
4. cos 150°=cos(90°+60°)=cos 90°×cos 60°- sin 90°×sin 60°=
=0×1/2-1×√3/2= -√3/2
sin 120°=sin(90°+30°)=sin 90°×cos 30°+cos 90°×sin 30°=
=1×√3/2+0×1/2=√3/2
(cos 150°+cos 30°)(sin 120°- sin 60°)=
=( -√3/2+√3/2)(√3/2-√3/2)=
=0×0=0
