已知tanα=3,求2/3sin²α+1/4sin²α的值 已知1/(tanα-1）=1,求1/(1+sinαcosα)的值

已知tanα=3,求2/3sin²α+1/4sin²α的值 已知1/(tanα-1）=1,求1/(1+sinαcosα)的值
已知tanα=3,求2/3sin²α+1/4sin²α的值 已知1/(tanα-1）=1,求1/(1+sinαcosα)的值

已知tanα=3,求2/3sin²α+1/4sin²α的值 已知1/(tanα-1）=1,求1/(1+sinαcosα)的值
（1）
2/3sin²α+1/4sin²α
=11/12sin²α/(sin²α+cos²α)
=11/12tan²α/(tan²α+1)
=11/12*3²/(3²+1)
=33/40
（2）
由1/(tanα-1)=1可得tanα=2
1/(1+sinαcosα)
=(sin²α+cos²α)/(sin²α+cos²α+sinαcosα)
=(tan²α+1)/(tan²α+1+tanα)
=(2²+1)/(2²+1+2)
=5/7

2/3sin²α+1/4sin²α=(2/3sin²α+1/4sin²α)/1=(2/3sin²α+1/4sin²α)/(cos²α+sin²α)=(2/3tan²α+1/4tan²α)/(
1+tan²α)=(33/4)/10=33/40