Question

How would you simplify this expression: 2sin2Acos2A?

Answer 1

is it \(2\sin(2A)\cos(2A)\)?

Answer 2

we know that 2 sin x cos x = sin (2x).
so 2 sin (2a)cos(2a) = sin (2*2a) = sin (4a)

Answer 3

i knew that 2 sinx cos x = sin (2x), i was hoping if someone could explain why?

Answer 4

it comes from the sine angle addition formula
sin ( x + y ) = sin x cos y + cos x sin y

Answer 5

then if we substitute into the formula
sin (x + x ) = sin x cos x + cos x sin x = 2 sin x cos x

Answer 6

YES! thank you :)