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计算:sin65°+sin15°sin10°sin25°-cos15°cos80°的值为.

题目详情
计算:
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
计算:
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
计算:
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
计算:
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
计算:
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
sin65°+sin15°sin10°
sin25°-cos15°cos80°
的值为 ______.
sin65°+sin15°sin10°
sin25°-cos15°cos80°
sin65°+sin15°sin10° sin25°-cos15°cos80° sin65°+sin15°sin10° sin65°+sin15°sin10° sin25°-cos15°cos80° sin25°-cos15°cos80°
▼优质解答
答案和解析
sin65°+sin15°sin10°
sin25°-cos15°cos80°

=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°+sin15°sin10°
sin25°-cos15°cos80°

=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°+sin15°sin10°
sin25°-cos15°cos80°

=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°+sin15°sin10°
sin25°-cos15°cos80°

=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°+sin15°sin10°
sin25°-cos15°cos80°

=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°+sin15°sin10°
sin25°-cos15°cos80°
sin65°+sin15°sin10° sin25°-cos15°cos80° sin65°+sin15°sin10° sin65°+sin15°sin10° sin65°+sin15°sin10° sin25°-cos15°cos80° sin25°-cos15°cos80° sin25°-cos15°cos80°
=
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )

=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
sin65°-
1
2
(cos25°-cos5° )
sin25°-
1
2
(cos95°+cos65° )
sin65°-
1
2
(cos25°-cos5° ) sin25°-
1
2
(cos95°+cos65° ) sin65°-
1
2
(cos25°-cos5° ) sin65°-
1
2
(cos25°-cos5° ) sin65°-
1
2
1 2 1 1 1 2 2 2 (cos25°-cos5° ) sin25°-
1
2
(cos95°+cos65° ) sin25°-
1
2
(cos95°+cos65° ) sin25°-
1
2
1 2 1 1 1 2 2 2 (cos95°+cos65° )
=
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°

=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°
1
2
sin65°+
1
2
cos5°
1
2
sin25°-
1
2
cos95°
1
2
sin65°+
1
2
cos5°
1
2
sin65°+
1
2
cos5°
1
2
1 2 1 1 1 2 2 2 sin65°+
1
2
1 2 1 1 1 2 2 2 cos5°
1
2
sin25°-
1
2
cos95°
1
2
sin25°-
1
2
cos95°
1
2
1 2 1 1 1 2 2 2 sin25°-
1
2
1 2 1 1 1 2 2 2 cos95°
=
cos25°+cos5°
cos65°-cos95°

=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
cos25°+cos5°
cos65°-cos95°
cos25°+cos5° cos65°-cos95° cos25°+cos5° cos25°+cos5° cos25°+cos5° cos65°-cos95° cos65°-cos95° cos65°-cos95°
=
2cos15°cos10°
2sin80°sin15°

=cot15°
=tan75°=2+
3

故答案为:2+
3
2cos15°cos10°
2sin80°sin15°
2cos15°cos10° 2sin80°sin15° 2cos15°cos10° 2cos15°cos10° 2cos15°cos10° 2sin80°sin15° 2sin80°sin15° 2sin80°sin15°
=cot15°
=tan75°=2+
3

故答案为:2+
3
3
3
3
3 3
故答案为:2+
3
3
3
3
3 3