(Ⅰ)计算:sin25π6+cos25π3+tan(-25π4);(Ⅱ)已知tanα=3,求4sinα-2cosα5cosα+3sinα的值.-数学

题目简介

(Ⅰ)计算:sin25π6+cos25π3+tan(-25π4);(Ⅱ)已知tanα=3,求4sinα-2cosα5cosα+3sinα的值.-数学

题目详情

(Ⅰ)计算:sin
25π
6
+cos
25π
3
+tan(-
25π
4
)

(Ⅱ)已知tanα=3,求
4sinα-2cosα
5cosα+3sinα
的值.
题型:解答题难度:中档来源:不详

答案

(Ⅰ)sinclass="stub"25π
6
+cosclass="stub"25π
3
+tan(-class="stub"25π
4
)=sinclass="stub"π
6
+cosclass="stub"π
3
-tanclass="stub"π
4
=class="stub"1
2
+class="stub"1
2
-1=0
…(4分)
(Ⅱ)显然cosα≠0
class="stub"4sinα-2cosα
5cosα+3sinα
=
class="stub"4sinα-2cosα
cosα
class="stub"5cosα+3sinα
cosα
=class="stub"4tanα-2
5+3tanα
=class="stub"4×3-2
5+3×3
=class="stub"5
7
…(8分)

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