已知tanα=2,求cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)的值我先化简了 可还做不出
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![已知tanα=2,求cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)的值我先化简了 可还做不出](/uploads/image/z/8798539-67-9.jpg?t=%E5%B7%B2%E7%9F%A5tan%CE%B1%3D2%2C%E6%B1%82cos%28%CE%B1-7%CF%80%2F2%29%2B2sin%28%CF%80-3%CE%B1%29%2Fcsc%28%CF%80%2B%CE%B1%29%2Bsec%28%CF%80%2F2%2B%CE%B1%EF%BC%89%E7%9A%84%E5%80%BC%E6%88%91%E5%85%88%E5%8C%96%E7%AE%80%E4%BA%86+%E5%8F%AF%E8%BF%98%E5%81%9A%E4%B8%8D%E5%87%BA)
已知tanα=2,求cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)的值我先化简了 可还做不出
已知tanα=2,求cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)的值
我先化简了 可还做不出
已知tanα=2,求cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)的值我先化简了 可还做不出
数理答疑团为你解答,希望对你有所帮助.
cos(α-7π/2)+2sin(π-3α)/csc(π+α)+sec(π/2+α)
=cosα cos(7π/2) + sinα sin(7π/2) + 2[sinπ cos(3α) - cosπsin(3α)]sin(π+α)+ 1/cos(π/2+α)
=cosα cos(π/2) + sinα sin(π/2) + 2[sinπ cos(3α) - cosπsin(3α)](sinπcosα +cosπsinα)
+ 1/[cos(π/2)cosα - sin(π/2)sinα ]
=0+sinα+2sin(3α) (-sinα) + 1/[0 - sinα ]
= sinα-2sinαsin(3α) - 1/sinα
=sinα-2sinαsin(α+2α) - 1/sinα
=sinα-2sinα(sinαcos2α+cosαsin2α) - 1/sinα
=sinα-2sinα[sinα(1-2sin²α)+2cos²αsinα] - 1/sinα
=sinα-2sinα[sinα-2sin³α+2cos²αsinα] - 1/sinα
tanα=2 sinα/cosα = 2 sin²α/cos²α =4
sin²α+cos²α =1
sin²α = 4/5
cos²α =1/5
sinα= 2√5/5 ,cosα =√5/5
或sinα= -2√5/5 ,cosα = -√5/5
原式=自己算