Answer:
see explanation
Explanation:
Using the sum/ difference → product formula
cos x - cos y = - 2sin(
)sin (
)
sin x - sin y = 2cos (
)sin (
)
Given
(cosA - cosB)² + (sinA - sinB )²
= [ - 2sin(
)sin(
) ]² + [ 2cos(
)sin(
) ]²
= 4sin² (
)sin² (
) + 4cos² (
)sin² (
)
= 4sin² (
)[ sin² (
) + cos² (
) ← sin²x + cos²x = 1
= 4sin² (
) × 1
= 4sin² (
) = right side ⇒ proven