已知sinx-cosx=1/2,求(sinx+cosx)2的值 已知sinx+cosx=1/5，x属于，求tanx的值
\u5df2\u77e51-cosx+sinx/(1+cosx+sinx)=-2,\u5219sinx\u7684\u503c\u4e3a1-cosx+sinx/(1+cosx+sinx)=-2
1-cosx+sinx=-2(1+cosx+sinx)
3sinx+3=-cosx
\u4e24\u8fb9\u5e73\u65b9\u5f97
9(sin^2,x+2sinx+1)=cos^2,x=1-sin^2,x
10sin^2,x+18sinx+8=0
2(5sinx+4)(sinx+1)=0
sinx=-4/5\u6216\u8005sinx=-1(\u820d\u53bb,\u56e0\u4e3a\u4ee3\u5165\u539f\u5f0f\u5206\u6bcd\u4e3a0)
sinx\u7684\u503c\u4e3a-4/5
\u7531sinx+cosx=1/5\uff0c\u5f97sinx=1/5-cosx
\u4ee3\u5165sin2x+cos2x=1\u5f97\uff085cosx-4\uff09\uff085cosx+3\uff09=0
\u2234cosx=4/5\u6216cosx=-3/5
\u5f53cosx=4/5\u65f6\uff0c\u5f97sinx=-3/5\uff0c\u6240\u4ee5tanx=-3/4
\u5f53cosx=-3/5\u65f6\uff0csinx=4/5\uff0c\u6240\u4ee5tanx=-4/3
\u6ca1\u6709\u89c4\u5b9aX\u7684\u8303\u56f4\uff0c\u6240\u4ee5\u6709\u4e24\u4e2a\u503c
两边平方得
sin²x-2sinxcosx+cos²x=1/4
2sinxcosx=3/4
1+2sinxcosx=7/4
sin²x+2sinxcosx+cos²x=7/4
∴(sinx+cosx)²=7/4
∵sinx-cosx=1/2
(sinx-cosx)^2=1/4
1-2sinxcosx=1/4
2sinxcosx=1-1/4
2sinxcosx=3/4
∴(sinx+cosx)^2=1+2sinxcosx
=1+3/4
=7/4
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绛旓細瑙 鏈sinx-cosx=1/2銆傚钩鏂瑰緱1-2sinx*cosx=1/4,鍗硈inx*cosx=3/8 鎵浠in²x+cos²x=1 1 sinx*cosx=3/8 2 涓ゅ紡鐩搁櫎寰 tanx-1/tanx=8/3 鏁寸悊寰 3tan²x-8 tanx-3=0 寰 tanx=-1/3鎴 tanx=3 鍙 tanx=2tanx/2/(1-3tan²x/2)tanx/2=(-1-鈭...
