已知tanα=2,求3sin(π+α)+cos(-α)/4sin(-α)-cos(9π+α)的值

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已知tanα=2,求3sin(π+α)+cos(-α)/4sin(-α)-cos(9π+α)的值

已知tanα=2,求3sin(π+α)+cos(-α)/4sin(-α)-cos(9π+α)的值
已知tanα=2,求3sin(π+α)+cos(-α)/4sin(-α)-cos(9π+α)的值

已知tanα=2,求3sin(π+α)+cos(-α)/4sin(-α)-cos(9π+α)的值
先利用诱导公式化简:
[3sin(π+α)+cos(-α)]/[4sin(-α)-cos(9π+α)]
=(-3sinα+cosα)/(-4sinα+cosα) 分子、分母同时除以cosα
=(-3tanα+1)/(-4tanα+1)
=5/7.