Question

 1/81^ (cosx)= 9^( 2sin2x)

Answer 1

1/81 = 9^(-2)
9^(-2cosx)=9^2sin2x
-2cosx=2sin2x
sin2x+cosx=0
2sinxcosx+cosx=0
cosx(2sinx+1)=0
cosx=0                              sinx= -1/2
x=π/2 + πk, k∈Z                 x= -π/6 + 2πn, n∈Z