简化三角函数!Simplify the expression.cos(2 tan^−1 (x))

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简化三角函数!Simplify the expression.cos(2 tan^−1 (x))

简化三角函数!Simplify the expression.cos(2 tan^−1 (x))
简化三角函数!
Simplify the expression.
cos(2 tan^−1 (x))

简化三角函数!Simplify the expression.cos(2 tan^−1 (x))
令θ=tan^-1(x)
则tanθ=x,cos[2tan^-1(x)]=cos2θ
由万能公式
cos2θ=(1-tan²θ)/(1+tan²θ)
=(1-x²)/(1+x²)
于是
cos[2tan^-1(x)]=(1-x²)/(1+x²)

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