Sin(x+派/2)=1/3则cos(x+7派/1 - 知识问答

Sin(x+派/2)=1/3则cos(x+7派/12)的值为?

1个回答

Sin(x+π/2)=cosx=1/3,则
sinx=土2√2/3,
cos(7π/12)=cos(π/3+π/4)=(√2-√6）/4,
sin(7π/12)=(√2+√6）/4,
∴cos(x+7π/12)=cosxcos(7π/12)-sinxsin(7π/12)
=（√2-√6）/12干（4+4√2）/12
=（-4-3√2-√6）/12,或（4+5√2-√6）/12.

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