no it is very different u can check it by taking a simple example like take a number apply 2 times log and in second way take 1 time log and multiply it 2 times . u can see large differnce so

sin^2x is not equal to sinx * sinx . just remember ur trignometry class if it is that much simple then why we apply cos2x formulae to calculate it just multipy two times and get result if u do this all trignometric identity gone wrong.