高中数学人教A版必修4练习3.1.2 两角和与差的正弦、余弦、正切公式 课堂强化 Word版含解析

.已知α∈, α=,则 =( ) . .-.- 解析:由于 α=,且 α∈(,π), 则 α=-,∴ α=-. ∴(α+)=α+- α)=. 答案: .若(α+β) β-(α+β) β=,则(α+β)+(α-β)等于( ) . .- . .± 解析:∵(α+β) β-(α+β) β=(α+β-β)= α=,∴(α+β)+(α-β)= α β+ α β+ α β- α β= α β=. 答案: .(θ+°)+(θ+°)-(θ+°)等于( ) .± . .- . 解析:原式=[°+(θ+°)]+(θ+°)-(θ+°) =-(θ+°)+(θ+°)+(θ+°) =(θ+°) °-(θ+°) °+(θ+°) =(θ-°)+(θ+°)=. 答案: °- ° °+ °)=. 解析:原式=°+ °)=°- °+ ° °) =(°-°)= °=. 答案: .已知α为锐角,且(α+β)=,(α-β)=,则角α等于. 解析:∵ α= [(α+β)+(α-β)] = ==-, ∴α=-+π(∈),∴α=-+(∈). 又∵α 为锐角,∴α=-=. 答案: .求 °°+ °°- °的值. 解:原式= °( °+ °)- ° = °°+(()) °)) -° = °( °°+ °· °)- ° = °(°+°)- ° =° °)· °- °)) =·° °- ° ° °) =·°) =·° °)=.

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