化简:sin^2α×tanα+cos^2α×cotα+2sinα×cosα
问题描述:
化简:sin^2α×tanα+cos^2α×cotα+2sinα×cosα
答
原式=sin^2a*sina/cosa+cos^2a*cosa/sina+2sina*cosa=sina^3a/cosa+cos^3a/sina+2sina*cosa=(通分)(sin^4a+cos^4a+2sin^2a*cos^2a)/sina*cosa=(sin^2a+cos^2a)^2/sina*cosa=1/sina*cosa