Question

已知TAN2θ =-2根号2 θ∈(π/2,π) (1)求TANθ的值 (2)

一、已知TAN2θ =-2根号2 θ∈(π/2,π) (1)求TANθ的值 (2)求[2COS^2(θ/2-SINθ-1)]/[根号2SIN(θ+π/4)]的值。

Answer 1

1. 已知tan2θ=-2√2
则tan2θ=2tanθ/(1-tan²θ)
θ∈(π/2,π) ，则tan θ>0
2tanθ=(1-tan²θ)(-2√2)
√2tan²θ-tanθ-√2=0
(√2tanθ+1)(tanθ-√2)=0
解得tanθ=√2
2. [2COS^2(θ/2)-SINθ-1]/[根号2SIN(θ+π/4)]
=(cosθ-sinθ)/(sinθ+cosθ)
=(1-tanθ)/(1+tanθ)
=(1-√2)/(1+√2)
=(1-√2)²/(1-2)
=2√2-3
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