Question

设tan(α+β)=3 ,问3cos^2(α+β)+3sin(α+β)cos(α+β)-sin^2(α+β) 的值能否为

Answer 1

tan(α+β)=3------------sin(α+β)=3cos(α+β)

3cos^2(α+β)+3sin(α+β)cos(α+β)-sin^2(α+β)=3cos^2(α+β)+3*3cos(α+β)cos(α+β)-[3cos(α+β)]^2=3cos^2(α+β),要值为自然数,而0