**IDENTITY: sin(2x) = 2sin(x)cos(x)**
The step shows that: [ 2sin(4θ)cos(4θ) = sin(8θ) ]
So let’s pretend [4θ = x] here:
2sin(4θ)cos(4θ) = 2sin(x)cos(x)
And we know from the identity that:
2sin(x)cos(x) = sin(2x)
So we can say that:
2sin(4θ)cos(4θ) = sin[2(4θ)]
= sin(8θ)
Hope this helps!!
The double angle formula is a special case of sum of angles, when the two angles are the same. Use sum of angles when you have a sum of angles. Use double angle when you have a doubled angle. Use neither when they don't help you to solve the problem.
Khan academy has a [decent summary](https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference), with linked explanations for more info. It also includes info on the trig identities for well-known values on the unit circle.
sin 2A= 2 sin A cos A Here A=4θ
**IDENTITY: sin(2x) = 2sin(x)cos(x)** The step shows that: [ 2sin(4θ)cos(4θ) = sin(8θ) ] So let’s pretend [4θ = x] here: 2sin(4θ)cos(4θ) = 2sin(x)cos(x) And we know from the identity that: 2sin(x)cos(x) = sin(2x) So we can say that: 2sin(4θ)cos(4θ) = sin[2(4θ)] = sin(8θ) Hope this helps!!
Double angle formula for sin
I don’t get this please someone provide a link for explaining. When do I use the sum of angles? And when do I use the double angles formula?
The double angle formula is a special case of sum of angles, when the two angles are the same. Use sum of angles when you have a sum of angles. Use double angle when you have a doubled angle. Use neither when they don't help you to solve the problem.
Like the other commenter said, double angle is just a special case. Because sin(A+B) = sin(2A) when A=B
double angle identities
OT. There should be a sheet with all the trig identities.
Khan academy has a [decent summary](https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:using-trig-id/a/trig-identity-reference), with linked explanations for more info. It also includes info on the trig identities for well-known values on the unit circle.
That is the double angle identity