Taking odd degrees only, find sin²1° + sin²3° + sin²5° + … + sin²89°.

22 1/2. 45 terms: 22 complementary pairs (1^°,89^°), ,(43^°,47^°) give 22, plus ^2 45^° = 12.

Taking odd degrees only, find si $n^{2}$ 1° + si $n^{2}$ 3° + si $n^{2}$ 5° + … + si $n^{2}$ 89°.

Competition practiceTrigonometry

45 terms: 22 complementary pairs

(1^{\circ}, 8 9^{\circ}), \dots, (4 3^{\circ}, 4 7^{\circ})

give 22, plus

sin^{2} 4 5^{\circ} = \frac{1}{2}

Answer: B) 22 1/2

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