Question

己知tanx=2,求2/3sin^2x+1/4cos^2x的值

Answer 1

2/3sin²x+1/4cos²x
=2/3(sin²x+cos²x)/sin²x+1/4*(sin²x+cos²x)/cos²x
=2/3(1+1/4)+1/4*(4+1)
=5/6+5/4
=25/12

Answer 2

2/3sin^2x+1/4cos^2x=(2/3sin^2x+1/4cos^2x)/(sin^2x+cos^2x)，
注：根据sin^2x+cos^2x=1和sinx/cosx=tanx得到
分子分母同时除以cos^2x得
=(2/3tan^2x+1/4)/(tan^2x+1)
=(2/3*4+1/4)/5
=175/12