化简(cos⁴7°30′-sin⁴7°30′)(sin23°cos8°-sin67°sin8°)
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/10/02 06:37:13
化简(cos⁴7°30′-sin⁴7°30′)(sin23°cos8°-sin67°sin8°)=A、1/4B、-1/4C、1D、-1
如题
如题
A、1/4
(cos⁴7°30′-sin⁴7°30′)(sin23°cos8°-sin67°sin8°)
=(cos²7°30′-sin²7°30′)(cos²7°30′+sin²7°30′)(sin23°cos8°-cos23°sin8°)
=(cos²7°30′-sin²7°30′)(sin(23°-8°)
=cos(2*7°30′)sin15°
=cos15°sin15°
=1/2*sin(2*15°)
=1/2*sin30°
=1/2*1/2
=1/4
(cos⁴7°30′-sin⁴7°30′)(sin23°cos8°-sin67°sin8°)
=(cos²7°30′-sin²7°30′)(cos²7°30′+sin²7°30′)(sin23°cos8°-cos23°sin8°)
=(cos²7°30′-sin²7°30′)(sin(23°-8°)
=cos(2*7°30′)sin15°
=cos15°sin15°
=1/2*sin(2*15°)
=1/2*sin30°
=1/2*1/2
=1/4
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