Sin²(π/2-x)-cos(π/2-x)cosx=0
cos²x-cos²x=0
0=0⇒x∈(-∞;∞)
6cos²x+26sinxcosx-10sin²x-10cos²x=0
10sin²x-26sinxcosx+4cos²x=0 /2cos²x≠0
5tg²x-13tgx+2=0
tgx=a
5a²-13a+2=0
D=169-40=129
a1=(13-√129)/10⇒tgx=(13-√129)/10⇒x=arctg(13-√129)/10+πn
a2=(13+√129)/10⇒tgx=(13+√129)/10⇒x=arctg(13+√129)/10+πn
Если 2sin²x-7sin(π/2-x)-5=0,то
2sin²x-7cosx-5=0
2(1-cos²x)-7cosx-5=0
2cos²x+7cosx+3=0
cosx=a
2a²+7a+3=0
D=49-24=25
a1=(-7-5)/4=-2,5∉[-1;1]
a2=(-7+5)/4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn
№2
а) (4*3-1*5)/(5*3) = (12-5)/15 = 7/15
б) (3*3-1*4)/(4*3) = (9-4)/12 = 5/12
в) (4*4-3*5)/(5*4) = (16-15)/*20 = 1/20
г) (3*9-4*4)/(4*9) = (27-16)/36 = 11/36
№3
а) (9-2*2)/14 = (9-4)/14 = 5/14
б) (5-1*4)/12 = (5-4)/12 = 1/12
в) (7-2*2)/10 = (7-4)/10 = 3/10 = 0,3
г) (17-1*10)/100 = (17-10)/100 = 7/100 = 0,07
3+x=4
x= 4-3
x=1
8-x=2
-x=2-8
-x=-6
x=6
С1=πD
C2=π(D+1)=πD+π
C2-C1=πD+π-πD=π=3,14 м
Ответ: на 3,14 м.