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2 Answers
- davidLv 77 years agoFavorite Answer
Sin 10 = cos 80 ... cofunction identity
sin 20 = cos 70
sin 30 = cos 60
sin 40 = cos 50
sin^2 10 + sin^2 20 + sin^2 30 + sin^2 40 + cos^2 40 + cos^2 30 + cos^2 20 + cos^2 10
= (sin^2 10 + cos^2 10) + (sin^2 20 + cos^2 20) + (sin^2 30 + cos^2 30) + (sin^2 40 + cos^2 40)
= 1 + 1 + 1 + 1 = 4 << answer
- MARK BLv 77 years ago
sin²10 + sin²80
= sin²10 + 1 - cos²80
= sin²10 + 1 - sin²10 . . . because cos(90-x) = sin(x)
= 1
Similarly sin²20 + sin²70 = 1
sin²30 + sin²60 = 1
sin²40 + sin²50 = 1
So your answer is 1 + 1 + 1 + 1 = 4
