已知α为锐角,满足sin²α+cos²α=1,sinα=(90º-α),根据上述结论解答下列问题(1)求sin²36º+sin²54º的值(2)求sin²1º+sin²2º+sin²3º+····+sin²88&ord

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已知α为锐角,满足sin²α+cos²α=1,sinα=(90º-α),根据上述结论解答下列问题(1)求sin²36º+sin²54º的值(2)求sin²1º+sin²2º+sin²3º+····+sin²88&ord

已知α为锐角,满足sin²α+cos²α=1,sinα=(90º-α),根据上述结论解答下列问题(1)求sin²36º+sin²54º的值(2)求sin²1º+sin²2º+sin²3º+····+sin²88&ord
已知α为锐角,满足sin²α+cos²α=1,sinα=(90º-α),根据上述结论解答下列问题
(1)求sin²36º+sin²54º的值
(2)求sin²1º+sin²2º+sin²3º+····+sin²88º+sin²89º的值

已知α为锐角,满足sin²α+cos²α=1,sinα=(90º-α),根据上述结论解答下列问题(1)求sin²36º+sin²54º的值(2)求sin²1º+sin²2º+sin²3º+····+sin²88&ord
因为 sinα=cos(90º-α),
所以 sin54º=cos(90º-54º)=cos36º,
所以 sin²36º+sin²54º
=sin²36º+cos²36º ( sin²α+cos²α=1 )
=1.
同理可得:
sin²1º+sin²89º=1
sin²2º+sin²88º=1
.
sin²44º+sin²46º=1
sin²1º+sin²2º+sin²3º+····+sin²88º+sin²89º
=44*1+sin²45º.

sin²45º+sin²45º=1
2sin²45º=1
sin²45º=1/2=0.5.
所以sin²1º+sin²2º+sin²3º+····+sin²88º+sin²89º
=44.5.