已知sin(

+2α)•sin(

-2α)=

,α∈(

,

),求2sin
2α+tanα-cotα-1的值.
【答案】
分析:利用誘導(dǎo)公式和二倍角公式化簡sin(

+2α)•sin(

-2α)=

為cos4α=

.求出α值,代入化簡2sin
2α+tanα-cotα-1后的表達式,求解即可.
解答:解:由sin(

+2α)•sin(

-2α)=sin(

+2α)•cos(

+2α)=

sin(

+4α)=

cos4α=

,
得cos4α=

.
又α∈(

,

),所以α=

.
于是2sin
2α+tanα-cotα-1=-cos2α+

=-cos2α+

=-(cos2α+2cot2α)=-(cos

+2cot

)
=-(-

-2

)=


.
點評:本題考查二倍角的正弦,弦切互化,考查計算能力,是基礎(chǔ)題.
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