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Answer:
There is a correction in your question.
Step-by-step explanation:
alpha = A & beta = B
Here,
=> (cosA - cosB)² + (sinA - sinB)²
=> cos²A + cos²B - 2cosAcosB + sin²A + sin²B - 2sinAsinB
=> (cos²A + sin²A) + (cos²B + sin²B) - 2cosAcosB - 2sinAsinB
=> 1 + 1 - 2cosAcosB - 2sinAsinB
=> 2 - 2(cosAcosB + sinAsinB)
{cosAcosB+sinAsinB=cos(A-B)}
=> 2 - 2cos(A - B)
=> 2(1 - cos(A - B))
{1 - cosx = 2sin²(x/2)}
=> 2(2sin²(A-B)/2}
=> 4sin²(A-B)/2 proved
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