Questions: 1 - cos 2 x / 2 can be simplified to: 1/2 - cos z cos^2 z sin^3 z 1-cos a

Solution Steps

The double-angle identity for cosine states that: \[ \cos 2x = 1 - 2\sin^2 x \] This can be rearranged to express \( \sin^2 x \) in terms of \( \cos 2x \): \[ \sin^2 x = \frac{1 - \cos 2x}{2} \]

The given expression is: \[ \frac{1 - \cos 2x}{2} \] Using the identity from Step 1, we can rewrite this as: \[ \frac{1 - \cos 2x}{2} = \sin^2 x \]

The simplified form of the expression is \( \sin^2 x \). Now, compare this with the provided options:

• \( \frac{1}{2} - \cos z \) does not match.
• \( \cos^2 z \) does not match.
• \( \sin^3 z \) does not match.
• \( 1 - \cos a \) does not match.

None of the provided options match the simplified form \( \sin^2 x \).

Final Answer