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inna [77]
3 years ago
10

Prove that:

Mathematics
1 answer:
Monica [59]3 years ago
3 0

Recall that

sin²(<em>x</em>) = (1 - cos(2<em>x</em>))/2

so that

sin²(7<em>π</em>/8) = (1 - cos(7<em>π</em>/4))/2

sin²(5<em>π</em>/8) = (1 - cos(5<em>π</em>/4))/2

Then

sin²(7<em>π</em>/8) + sin²(5<em>π</em>/8) = (1 - cos(7<em>π</em>/4) + 1 - cos(5<em>π</em>/4))/2

… = 1 - 1/2 (cos(7<em>π</em>/4) + cos(5<em>π</em>/4))

… = 1 - 1/2 (1/√2 - 1/√2)

… = 1

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