Ecuaciones

34) cos 2x=cos²x
cosx+x=cos²x
cos²x-sen2x=cos²x
cos²x-1-cos2x=cos²x
cos²x-1+cos2x-cos2x=0
cos²x-1=0
cos²x=1
cosx=1
x=arccos1
x=0° x=180°
35) tgx+45°=1+sen 2xtgx+tg45°1-tgx tg45°=1+2senx cosx
tgx+11-tgx=1+2senx cosx
tgx+1=(1+2senx cosx)(1-tgx)
tgx+1=1-tgx+2senx cosx-2senx cosx tgx
2tgx=2senx cosx-2senx cosx senxcosx
2tgx=2senx cosx-2sen²xsenxcosx=senx cosx-sen²x
1=senx cosx-sen2xcosxsenx
1=cos²x-senx cosx
1=cos²x-1-cos2x cosx
1-cosx2=(1-cos2x cosx)²
(1-cos2x)=1-cos2x cos2x
1-2cos2x+cos4x=cos2x-cos4x
2cos4x-3cos2x+1=0cos²x=--3±-32-42122
cos²x=3±14
cos²x=1 cos²x=12
x=arccos1 x=arccos12
x=0° x=45°
x=180° x=135°
36) sen60-x-sen60+x=32
sen60cosx-senx cos60-sen60 cosx+senx cos60=32
32cosx-12senx-32cosx+12senx=32
3cosx-senx-3cosx-senx=3
-2senx=3
senx=-32
x=arcsen-32
x=60° x=-60°
x=60° x=300°
37)sen30+x-cos60+x=-32
sen30 cosx+senx cos30-cos60 cosx-sen60 senx=-32
12cosx+32senx-12cosx-32senx=-32
3senx+3senx=-3
23senx=-3
2senx=-1
senx=-12
x=arcsen-12
x=-30 x=180°+30°x=330° x=210°
38) tg45-x+ctg45-x=4
tg45-tgx1-tg45 tgx+1+tg45 tgxtg45-tgx=4
1-tgx1+tgx+1+tgx1-tgx=4
1-tgx2+1+tgx21+tgx1-tgx=4
1-tgx2+1+tgx2=41-tg2x1-2tgx+tg2x+1+2tgx+tg2x=4-4tg²x
2+2tg²x=4-4tg²x
-2+6tg2x=0
6tg²x=2
tg²x=13
tgx=13
x=arctg13
x=30° x=-30°
x=30° x=330°
39) senx senx2=1-cosx
senx 1-cosx2²=(1-cosx)²
sen²x1-cosx2=1-2cosx+cos²x
1-cos2x1-cosx2=1-2cosx+cos²x
1-cos2x1-cosx=1-2cosx+cos2x2
1-cosx-cos2x+cos3x=2-4cosx+2cos2x
cos3x=1-3cosx+3cos2x
40) senx2+cosx=1
1-cosx2=1-cosx
1-cosx2²=(1-cosx)²1-cosx2=1-2cosx+cos²x
1-cosx=1-2cosx+cos2x 2
1-cosx=2-4cosx+2cos²x
2cos²x-3cosx+1=0
cosx=--3±-32-42122
cosx=3±14
x=arccos⁡(1) x=arccos12
x=0° x=60°