(cosπ/8+sinπ/8)(cos^3π/8-sin^3π/8)
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(cosπ/8+sinπ/8)(cos^3π/8-sin^3π/8)
是要化简吗?
(cosπ/8+sinπ/8)(cos³3π/8-sin³3π/8)
=(cosπ/8+sinπ/8)(cosπ/8-sinπ/8)(cos²3π/8+cos3π/8sin3π/8+sin²3π/8)
=(cos²π/8-sin²π/8)(1+1/2sin3π/4)
=cosπ/4 × (1+1/2sin3π/4)
(老实说我觉得你应该知道cosπ/4和sin3π/4的值了……)
=cosπ/4 × (1+1/2sinπ/4)
=√2/2 × (1+√2/4)
=(2√2+1)/4
(cosπ/8+sinπ/8)(cos³3π/8-sin³3π/8)
=(cosπ/8+sinπ/8)(cosπ/8-sinπ/8)(cos²3π/8+cos3π/8sin3π/8+sin²3π/8)
=(cos²π/8-sin²π/8)(1+1/2sin3π/4)
=cosπ/4 × (1+1/2sin3π/4)
(老实说我觉得你应该知道cosπ/4和sin3π/4的值了……)
=cosπ/4 × (1+1/2sinπ/4)
=√2/2 × (1+√2/4)
=(2√2+1)/4
(cosπ/8+sinπ/8)(cos^3π/8-sin^3π/8)
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