1
sin10xsin2x-sin8xsin4x=0
1/2cos8x-1/2cos12x-1/2cos4x+1/2cos12x=0
1/2(cos8x-cos4x)=0
1/2*(-2sin2xsin6x)=0
sin2x=0⇒2x=πn,n∈z⇒x=πn/2,n∈z
sin6x=πk,k∈x⇒x=πk/6,k∈x
1)-π/6≤πn/2≤π/2
-1≤2n≤3
-1/2≤n≤3/2
n=0⇒x=0
n=1⇒x=π/2
2)-π/6≤πk/6≤π/2
-1≤k≤3
-1/6≤k≤3
k=0⇒x=0
k=1⇒x=π/6
k=2⇒x=π/3
k=3⇒x=π/2
2
a)√3sinx+cosx=√2
2(√3/2sinx+1/2cosx)=√2
sin(x+π/6)=√2/2
x+π/6=-π/4+2πn,n∈z⇒x=-5π12+2πn,n∈z
x+π/6=5π/4+2πk,k∈z⇒x=13π/12+2πk,k∈z
b)1-cos(x/2)=tg(x/4)
2sin²(x/4)=sin(x/4)/cos(x/4)
2sin²(x/4)cos(x/4)-sin(x/4)=0,cos(x/4)≠0
sin(x/4)*(2sin(x/4)cos(x/4)-1)=0
sin(x/4)=0⇒x/4=πn,n∈z⇒x=4πn,n∈z
sin(x/2)=1⇒x/2=π/2+2πk,k∈z⇒x=π+4πk,k∈z