cos 2x
cos^2 x – sin^2 x
cos 2x can be evaluated using the double-angle formula for cosine, which states that cos 2x = cos²x – sin²x. Alternatively, it can also be expressed as 1 – 2sin²x.
To use the double-angle formula, we first need to know the values of cos x and sin x. Once we have those, we can substitute them into the formula and simplify.
For example, let’s say cos x = 3/5 and sin x = 4/5.
Then, cos²x = (3/5)² = 9/25
and sin²x = (4/5)² = 16/25
So, cos 2x = cos²x – sin²x
= 9/25 – 16/25
= -7/25
Alternatively, using 1 – 2sin²x, we get:
cos 2x = 1 – 2sin²x
= 1 – 2(16/25)
= 1 – 32/25
= -7/25
Therefore, cos 2x = -7/25 when cos x = 3/5 and sin x = 4/5.
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