sinα=cos2α,α∈[π/2,π],求tanα

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sinα=cos2α,α∈[π/2,π],求tanα
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sinα=cos2α,α∈[π/2,π],求tanα
sinα=cos2α,α∈[π/2,π],求tanα

sinα=cos2α,α∈[π/2,π],求tanα
sinα=cos2α=1-2sin^2α
2sin^2α + sinα - 1 = 0
(sinα+1)(2sinα-1)=0
α∈[π/2,π],sinα>0,sinα+1>1
2sinα-1=0
sinα=1/2
tanα = -sinα/√(1-sin^2α) = -√3/3

因为sinα=cos2α,所以sinα=1-2sin²α,2sin²α+sinα-1=0,又因为α∈[π/2,π],所以sinα=1/2,tanα=根号3/3