To prove this identity, we can use the double angle identity for sine:
sin(2θ) = 2sin(θ)cos(θ)
So, let's set θ = π/16:
sin(π/8)cos(π/8) = sin(2π/16)
sin(π/8)cos(π/8) = sin(π/8)
This confirms that 2sin(π/8)cos(π/8) = sin(2π/16).
To prove this identity, we can use the double angle identity for sine:
sin(2θ) = 2sin(θ)cos(θ)
So, let's set θ = π/16:
sin(π/8)cos(π/8) = sin(2π/16)
sin(π/8)cos(π/8) = sin(π/8)
sin(π/8)cos(π/8) = sin(π/8)
This confirms that 2sin(π/8)cos(π/8) = sin(2π/16).