Question

I have just been told that (sin2x)^2=sin^2 2x HOW????

Answer 1

it's just a difference in notation\[\sin^2x=(\sin x)^2\]

Answer 2

they mean the same thing; two ways to write it

Answer 3

note:
this is \(not\) the same as\[\sin(x^2)\]

Answer 4

i.e.\[(\sin x)^2=\sin^2x\neq\sin(x^2)\]

Answer 5

that kind of goes against what I have learnt about exponents

Answer 6

I would of said (sin x)^2=sin^2 x^2

Answer 7

but sin() is just a function. its not another variable you can put the exponent on using that rule.

Answer 8

exactly^
if sin(x) were a variable (sin) times another variable (x) you could distribute
but in this case it is a function, and so cannot be simplified that way

Answer 9

what's really gonna cook you noodle is this notation... \(\sin^{-1}(x^2)\ne [sin(x^2)]^{-1} \)

Answer 10

thats what arcsin() is for