Expand the Trigonometric Expression 1-cos(a)

Problem

1−cos(a)

Solution

1. Identify the trigonometric identity for the half-angle or double-angle formula. The expression 1−cos(a) is a standard form used in power-reduction identities.

2. Apply the formula for the sine squared half-angle identity, which states sin2(θ)=(1−cos(2*θ))/2

3. Rearrange the identity by multiplying both sides by 2 to get 2*sin2(θ)=1−cos(2*θ)

4. Substitute θ=a/2 into the rearranged identity to match the given expression.

5. Conclude that 1−cos(a) expands (or transforms) into 2*sin2(a/2)

Final Answer

1−cos(a)=2*sin2(a/2)

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