2sin([latex] \frac{7 \pi }{2} [/latex]-x)*sinx=cosx на [[latex] \frac{7 \pi }{2} [/latex];5[latex] \pi [/latex]]

2sin(7π/2-x)*sinx=cosx -2cosx*sinx-cosx=0 -cosx(2sinx+1)=0 cosx=0⇒x=π/2+πn,n∈z 7π/2≤π/2+πn≤5π 7≤1+2n≤10 6≤2n≤9 3≤n≤4,5 n=3⇒x=π/2+3π=7π/2 n=4πx=π/2+4π=9π/2 sinx=-1/2⇒x=-π/6+2πn U x=-5π/6+2πn 7π/2≤-π/6+2πn≤5π 21≤-1+12n≤30 22≤12n≤31 11/6≤n≤31/12 n=2⇒x=-π/6+4π=23π/24 7π/2≤-5π/6+2πn≤5π 21≤-5+12n≤30 26≤12n≤35 13/6≤n≤35/12 нет решения