1.已知tan(π⼀4+α)=2,求 (1)tanα的值 (2)sin2α+sinα的平方+cos2α的值

2025-06-21 02:42:37
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回答1:

(tan a +tan b)/(1-tan a *tan b)

tan((π/4+α)=2
(1 + tanα)/(1-tanα) = 2
1 + tanα = 2(1 - tanα)
tanα = 1/3

sin2α+(sinα)^2+cos2α
=2sinαcosα + (sinα)^2 +(1-2(sinα)^2)
=1+2sinαcosα-(sinα)^2
= 1+2(3/10) - 1/10
= 3/2 #