已知x是三角形的内角,且sinx+cosx=−1/5, (Ⅰ)求cosx的值; (Ⅱ)求tan(2x+π4)的值.
已知x是三角形的内角,且
sinx+cosx=−,
(Ⅰ)求cosx的值;
(Ⅱ)求
tan(2x+)的值.
数学人气:794 ℃时间:2019-11-22 23:26:59
优质解答
(Ⅰ)由-1<sinx+cosx<0得x∈(
,π)
又∵
| sinx+cosx=− | sin2x +cos2x=1 |
| |
解得:cosx=-
(Ⅱ)由(Ⅰ)得sinx=
=
∴tanx=
=-
∴tan2x=
=
=-
∴tan(2x+
)=
=-
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