(1)化简:sin(2π-α)sin(π+α)cos(-π-α)sin(3π-α)•cos(π-α)(2)求值sin500(1+3tan100).-数学

题目简介

(1)化简:sin(2π-α)sin(π+α)cos(-π-α)sin(3π-α)•cos(π-α)(2)求值sin500(1+3tan100).-数学

题目详情

(1)化简:
sin(2π-α)sin(π+α)cos(-π-α)
sin(3π-α)•cos(π-α)

(2)求值  sin500(1+
3
tan100)
题型:解答题难度:中档来源:不详

答案

(1)
sin(2π-α)sin(π+α)cos(-π-α)
sin(3π-α)•cos(π-α)

=
-sinα(-sinα)cos(π+α)
sin(π-α)•(-cosα)

=
sin2α(-cosα)
sinα•(-cosα)

=sinα;
(2)sin50°(1+
3
tan10°)
=sin50°(1+
3
class="stub"sin10°
cos10°

=sin50°•
cos10°+
3
sin10°
cos10°

=sin50°•
2(class="stub"1
2
cos10°+ 
3
2
 sin10°)
cos10°

=sin50°•class="stub"2sin40°
cos10°

=class="stub"2sin40°cos40°
cos10°

=class="stub"sin80°
cos10°

=class="stub"cos10°
cos10°

=1.

更多内容推荐