因為 sin α =2 cos α,
所以 tan α =2.
所以 (sin α)^2 +2 sinα cosα =[ (sin α)^2 +2 sin α cos α ] / [ (sin α)^2 +(cos α)^2 ]
=[ (tan α)^2 +2 tan α ] / [ (tan α)^2 +1 ]
=8/5.
= = = = = = = = =
以上計算可能有誤!
弦化切,即原式先除以 (sin α)^2 +(cos α)^2,然后分子分母同時除以 (cos α)^2.
= = = = = = = = =
解法2：
令 x =cos α,
則 sin α =2x.
所以 x^2 +(2x)^2 =1,
解得 x^2 =1/5.
所以 原式 =(2x)^2 +2 *2x *x
=8x^2
=8/5.
= = = = = = = = =
換元法.同角三角函數(shù)問題,實質(zhì)上是代數(shù)問題.