Question

已知tan(α+β)/2=√6 /2,cotα·cotβ=7/13,求cos(α-β)的值

Answer 1

cotα·cotβ=7/13tanαtanβ=13/7令(α+β)/2=A,(α-β)/2=B则A+B=α ,A-B=β ,tanA=√6/2 tanα=tan(A+B)=(tanA+tanB)/(1-tanAtanB) ,tanβ=tan(A-B)=(tanA-tanB)/(1+tanAtanB) ,tanαtanβ=(tanA+tanB)/(1-tanAta...