cos 2x
cos^2 x – sin^2 x
To find cos(2x), we can use the double-angle identity for cosine, which states that:
cos(2x) = cos²(x) – sin²(x)
Alternatively, we could use the angle addition formula for cosine, which states that:
cos(α + β) = cos(α)cos(β) – sin(α)sin(β)
In this case, we would treat 2x as the sum of two angles, so that:
cos(2x) = cos(x + x) = cos(x)cos(x) – sin(x)sin(x) = cos²(x) – sin²(x)
Either way, we end up with the same result: cos(2x) = cos²(x) – sin²(x). This formula can be used to simplify trigonometric expressions, or to find the value of cos(2x) for a particular value of x.
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