Use sum identities to derive one double angle identity for cosine

Hint: cos 2 Ф = cos (Ф+Ф)
Ф=theta

Step-by-step explanation:

The angle sum formula for cosine is ...

  cos(α+β) = cos(α)cos(β) -sin(α)sin(β)

When we have α = β = Ф, this becomes ...

  cos(Ф+Ф) = cos(Ф)cos(Ф) -sin(Ф)sin(Ф)

  cos(2Ф) = cos²(Ф) -sin²(Ф)

The "Pythagorean identity" can be used to write this in terms of sine or cosine.

  cos(2Ф) = (1 -sin²(Ф)) -sin²(Ф)

  cos(2Ф) = 1 -2sin²(Ф)

or

  cos(2Ф) = cos²(Ф) -(1 -cos²(Ф))

  cos(2Ф) = 2cos²(Ф) -1

step-by-step explanation:

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dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.