16(cosx)2 *(sinx)4 +16(sinx)2 *(cosx)4 =16
16*(cosx)2 *(sinx)2 [(sinx)2 +(cosx)2 ]=16
16*(cosx)2 *(sinx)2 =16
(cosx)2 *(sinx)2 =1
cosx * sinx = ±1
Then it's doesn't because if you need to get 1 there are to cases
(1) 1*1=1
It doesn't work because there is no x gives you cosx=sinx=1
(2) a number multiplied by his reciprocal equals 1
Which means you need to multiply a number smaller than with a number that is greater than one. It doesn't work because -1≤cosx,sinx≤1.
Pss* you can also use sin2x=2cosxsinx like this:
(Cosx)2 *(sinx)2 =1
[(Sin2x)2 ]/4=1
(Sin2x)2 =4
Sin2x=±2
Which doesn't work because -1≤sin2x≤1
*is used it like this:
sin2x=2cosxsinx
(sin2x)/2=cosx*sinx