tanθ+cotθ=3,则tan^2θ+secθcscθ+cot^2θ的值为

问题描述:

tanθ+cotθ=3,则tan^2θ+secθcscθ+cot^2θ的值为

tanθ+cotθ=3
(tanθ+cotθ)^=tan^2θ+2+cot^2θ=9
tan^2θ+2+cot^2θ=7
secθcscθ=1/(sinθcosθ)=sin^2θcos^2θ/sinθcosθ=tanθ+cotθ=3
两式相加,得解为10