The expression 1 – cos(2x) can be simplified using a trigonometric identity. According to the double angle formula, we know that:
- cos(2x) = 2cos²(x) – 1
Now, we can substitute this identity into our expression:
1 – cos(2x) = 1 – (2cos²(x) – 1)
Simplifying this further gives:
- 1 – 2cos²(x) + 1 = 2 – 2cos²(x)
Factoring out a 2, we have:
1 – cos(2x) = 2(1 – cos²(x))
Now, we can use another identity which states that:
- 1 – cos²(x) = sin²(x)
Therefore, we substitute this in:
1 – cos(2x) = 2sin²(x)
In conclusion, the expression 1 – cos(2x) simplifies to 2sin²(x). This identity is useful in various trigonometric applications, particularly in solving equations involving sine and cosine.