Question

1.Calculati cos 30°+2cos 60°+cos 150°.
2.Calculati cos 135°+sin 135°
3.Calculati 1/radical 3 cos pi/6-cos² pi/4
4.Calculati (sinx-cosx)²,stiind ca sin 2x=1
5.Calculati tgx,stiind ca cosx =2/3 si x€(0,pi/2)
6.Calculati tgx,stiind ca x€(0,pi/2) si sinx+3 cosx/cosx =4

DAU COROANA​

Answer 1

Răspuns:

Explicație pas cu pas:

1

cos150°=-cos30°

√3/2+2×1/2-√3/2=1

2

cos135°=cos(180°-45°)=-cos45°

sin 135°=sin 35°

cos 135°+sin 135°=sin 35°-co45°=√2/2-√2/2=0

3

1/√3 cos30°-cos²45°=1/√3×√3/2-1/2=1/2-1/2=0

4

(sinx-cosx)²=sin²x+2sinxcosx+cos²x=1+sin2x=1-1=0

5

tgx=sinx/cosx

sinx=√1-4/9=√5/3

tgx=√5/3×3/2=√5/2

6

(sinx+3cosx)/cosx=4

cosx(sinx/cosx+3)/cosx=4     tgx+3=4      tgx=1    x=45°