Consider the derivation of an alternate form of the cosine double angle identity. What is the error in this derivation?

In step 1, cos(2x) is equal to cos2(x) + sin2(x).
In step 2, sin2(x) should have been replaced with 1 + cos2(x).
In step 3, cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).
In step 4, 2cos2(x) – 1 should be 1 – 2cos2(x).

Error in step 3

Step-by-step explanation:

Correct derivation of the formula is as followed,

Step 1.

Cos(2x) = Cos²x - Sin²x

Step 2.

Cos²x - Sin²x = Cos²x - (1 - Cos²x)

Step 3.

Cos²x - (1 - Cos²x) = Cos²x - 1 + Cos²x

Step 4.

Cos²x - 1 + Cos²x = 2Cos²x - 1

There is an error in step 3 of the given derivation.

Cos²x - 1 - Cos²x should be Cos²x - 1 + Cos²x

step-by-step explanation:

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