已知α为锐角,且sin α+cos α=√5/2,求sin α·cos α的值

已知α为锐角,且sin α+cos α=√5/2,求sin α·cos α的值
已知α为锐角,且sin α+cos α=√5/2,求sin α·cos α的值

已知α为锐角,且sin α+cos α=√5/2,求sin α·cos α的值
两边都平方,得
（sin α+cos α）X（sin α+cos α）=5/4
sin αXsin α+cos αXcos α+2sin αcos α=5/4
即 1+2sin αcos α=5/4
得2sin αcos α=5/4-1=1/4
所以 sin αcos α=1/8

两边平方得1+2sinacosa=5/4
所以sinacosa=1/8