已知tanx=2,求(2/3)sin²x+(1/4)cos²x的值

已知tanx=2,求(2/3)sin²x+(1/4)cos²x的值
已知tanx=2,求(2/3)sin²x+(1/4)cos²x的值

已知tanx=2,求(2/3)sin²x+(1/4)cos²x的值
tanx=2
(2/3)sin^2(x)+(1/4)cos^2(x)
=[(2/3)sin^2(x)+(1/4)cos^2(x)]/1
=[(2/3)sin^2(x)+(1/4)cos^2(x)]/[sin^2(x)+cos^2(x)]
分子分母同除以cos^2(x)得：
原式=[(2/3)tan^2(x)+(1/4)]/[tan^2(x)+1]
=[(2/3)*4+(1/4)]/[4+1]
=[(8/3)+(1/4)]/5
=7/12