Question

已知tan α=2,求1+sin α cos α/ sin平方α+1的值

Answer 1

tanα=2 sinα/cosα=2 sinα=2cosα

sin²α+cos²α=1

(2cosα)²+cos²α=1

5cos²α=1

cos²α=1/5

(1+sinαcosα)/(sin²α+1)

=(1+2cos²α)/(1-cos²α+1)

=(1+2cos²α)/(2-cos²α)

=[1+2×(1/5)]/(2-1/5)

=(7/5)/(9/5)

=7/9