-7sin(π/2-2x)+9cosx+1=0
-7cos2x+9cosx+1=0
-7*(2cos²x-1)+9cosx+1=0
-14cos²x+7+9cosx+1=0
cosx=t
14t²-9t-8=0
D=81+448=529
t1=(9-23)/28=-1/2⇒cosx=-1/2
x=-2π/3+2πk,k∈z
x=2π/3+2πk,k∈z
t2=(9+23)/28=8/7⇒cosx=8/7>1 нет решения
-3π/2≤-2π/3+2πk≤π/3
-5≤12k≤6
-5/12≤k≤6/12
k=0 x=-2π/3
-3π/2≤2π/3+2πk≤π/3
-13≤12k≤-2
-13/12≤k≤-2/12
k=-1 x=2π/3-2π=-4π/3