已知x=5π/12,则sinx-cosx的值为?

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已知x=5π/12,则sinx-cosx的值为?已知x=5π/12,则sinx-cosx的值为?已知x=5π/12,则sinx-cosx的值为?已知x=5π/12,则:sinx-cosx=根号2*[(

已知x=5π/12,则sinx-cosx的值为?
已知x=5π/12,则sinx-cosx的值为?

已知x=5π/12,则sinx-cosx的值为?
已知x=5π/12,则:
sinx-cosx
=根号2*[(根号2)/2 *sinx - (根号2)/2 *cosx]
=根号2*sin(x- π/4)
=根号2*sin(5π/12 - π/4)
=根号2*sin(π/6)
=(根号2)/2

0.707

sinx-cosx=√2sin(x-π/4)
=√2sin(5π/12-π/4)
=√2sinπ/6
=√2/2

5π/12=π/4+π/6,可得其sin cos值
结果是√2/2

sinx-cosx=sin(x-pi/4)*2^1/2=√2sinpi/12=√2sin(pi/3-pi/4)=√2(sin60cos45-cos60sin45)=(√6-√2)/2

0.7071

-0.97689