求值：cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)

题目

求值：cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
学到三角恒等式的 诱导公式 那里
求值：cos(3π/8-θ)cos(5π/24-θ)+sin(π/8+θ)sin(7π/24+θ)
我算到一半算不下去了
π是派(pai)哦...
=2cos(3π/8-θ)cos(5π/24-θ)
=cos(3π/8-θ-5π/24+θ)+cos(3π/8-θ+5π/24-θ)
只是搞不懂这两步之间怎么变过去的...我自己就做到=2cos(3π/8-θ)cos(5π/24-θ) 这步

答案

注意关系3π/8-θ=π/2-(π/8+θ)
5π/24-θ=π/2-(7π/24+θ)
所以原式=cos(3π/8-θ)cos(5π/24-θ)+cos(3π/8-θ)sin(7π/24+θ)
=cos(3π/8-θ)cos(5π/24-θ)+cos(3π/8-θ)cos(5π/24-θ)
=2cos(3π/8-θ)cos(5π/24-θ)
=cos(3π/8-θ-5π/24+θ)+cos(3π/8-θ+5π/24-θ)
=cosπ/6+cos(7/12π-2θ)
这是积化合差公式
cosA*cosB=1/2[cos(A-B)+cos(A+B)]