已知,tan(π4+α)=3,计算:(1)tanα(2)2sinαcosα+3cos2α5cos2α-3sin2α(3)sinα•cosα-高三数学

题目简介

已知,tan(π4+α)=3,计算:(1)tanα(2)2sinαcosα+3cos2α5cos2α-3sin2α(3)sinα•cosα-高三数学

题目详情

已知,tan(
π
4
+α)=3,计算:
(1)tanα
(2)
2sinαcosα+3cos2α
5cos2α-3sin2α

(3)sinα•cosα
题型:解答题难度:中档来源:不详

答案

(1)∵已知tan(class="stub"π
4
+α)=3=class="stub"1+tanα
1-tanα
,∴tanα=class="stub"1
2

(2)由(1)可得tan2α=class="stub"2tanα
1-tan2α
=class="stub"1
1-class="stub"1
4
=class="stub"4
3

class="stub"2sinαcosα+3cos2α
5cos2α-3sin2α
=class="stub"sin2α+3cos2α
5cos2α-3sin2α
=class="stub"tan2α+3
5-3tan2α
=
class="stub"4
3
+3
5-3×class="stub"4
3
=class="stub"13
3

(3)sinα•cosα=class="stub"sinαcosα
cos2α+sin2α
=class="stub"tanα
1+tan2α
=
class="stub"1
2
1+class="stub"1
4
=class="stub"2
5

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