已知sina-3cosa=0,求2/3sin^2a+1/4cos^2的值

题目

已知sina-3cosa=0,求2/3sin^2a+1/4cos^2的值

答案

tana=3
2/3sin^2a+1/4cos^2
=[2/3sin^2a+1/4cos^2]/(sin²a+cos²a)
分子分母同除以cos²a
=[4/3tana+1/4]/[tan²a+1]
=(4+1/4)/10
=17/4 *1/10
=17/40