已知sinacosa=2/5且√cos=-cosa.则sina+cosa 1）已知sina+cosa=4/5,且π/2<a<π,求si...
sina+2cosa=\u221a5,\u5219cos2a sina+2cosa=\u221a5,\u5219cos2a\uff1f\u89e3\u7531sina+2cosa=\u221a5,
\u5f97sin^2a+4cos^2a+4sinacosa=5=5sin^2a+5cos^2a
\u52194sin^2a-4sinacosa+cos^2a=0
\u5373(2sina-cosa)^2=0
\u53732sina-cosa=0
\u5373tana=sina/cosa=1/2
\u5219cos2a
=(1-tan^2a)/(1+tan^2a)
=(1-1/4)/(1+1/4)
=3/5
(1)\u03c0/2<a<\u03c0
\u5219\uff1asina>0\uff1bcosa<0
sina+cosa=4/5,
cosa=4/5-sina
sin²a+cos²a=1
sin²a+(4/5-sina)²=1
2sin²a-8/5sina-9/25=0
2(sina-2/5)²=17/25
(sina-2/5)²=17/50
sina=2/5+\u221a34/10
cosa=4/5-sina=2/5-\u221a34/10
sina-cosa=\u221a34/5
(2)sin(a+b)=sinacosb+cossinb=1/2
sin(a-b)=sinacosb-cossinb=1/3
\u76f8\u52a0
2sinacosb=5/6
sinacosb=5/12
\u6240\u4ee5cosasinb=1/12
\u76f8\u9664
(sina/cosa)/(sinb/cosb)=5
tana/tanb=5
∴（sina+cosa）^2=sina^2+cosa^2+2sinacosa=1+(2/5)*2=9/5
又√cos>0
∴-cosa>0,从而cosa<0
1）若sina>0,则-1<sina+cosa<1
∴此时sina+cosa）^2<1<9/5(舍)
2）若sina<0,此时sina+cosa<0
∴sina+cosa=（3√5）/5
先求（sina+cosa）²，由于（sina+cosa）²=sina²+cosa²+2sinacosa=1+2×2/5=9/5，因为sina×cosa=2/5>0.所以sina>0,cosa>0.也就是(sina+cosa)>0,所以sina+cosa=9/5的开平方，取正值
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绛旓細鍗筹細sin2a=2sinacosa銆備竾鑳藉叕寮忔帹瀵硷細璁総an(A/2)=t銆俿inA=2t/(1+t^2) 锛圓鈮2k蟺+蟺锛宬鈭圸锛夈倀anA=2t/(1-t^2) 锛圓鈮2k蟺+蟺锛宬鈭圸锛夈cosA=(1-t^2)/(1+t^2) 锛圓鈮2k蟺+蟺 k鈭圸锛夈傚氨鏄sinA銆乼anA銆乧osA閮藉彲浠ョ敤tan(A/2)鏉ヨ〃绀猴紱褰撹姹備竴涓插嚱鏁板紡鏈鍊肩殑鏃跺欙紝灏...
绛旓細鍥犱负tana=sina/cosa=2锛屾墍浠ina=2cosa锛屽張鍥(sina)^2+(cosa)^2=1锛岃В寰梥ina=2鈭5/5锛宑osa=鈭5/5锛屾鏃sinacosa=2/5锛涘綋sina=-2鈭5/5锛宑osa=-鈭5/5鏃讹紝sinacosa=2/5銆傜患涓婃墍杩帮紝sinacosa=2/5銆
绛旓細sin2a=2sinacosa=2*3/5*cosa=6/5cosa cosa=鏍瑰彿涓嬶紙1-sin^2a锛=4/5鎴栬礋4/5 鍥犱负sina=3/5 鎵浠osa=4/5 鎵浠in2a=(6/5)*(4/5)=24/25
绛旓細sin2a=2sinacosa 鎵浠 (sina-cosa)^2=sina^+cosa^2+2sinacosa 鎳備簡鍚
绛旓細sina-cosa=鈭2 涓よ竟骞虫柟寰楋細sin²a+cos²a-2sinacosa=2 鍗筹細1-sin2a=2 鍒欙細sin2a=-1 绁濅綘寮蹇冿紒甯屾湜鑳藉府鍒颁綘锛屽鏋滀笉鎳傦紝璇稨i鎴戯紝绁濆涔犺繘姝ワ紒O(鈭鈭)O
绛旓細宸茬煡sina锛屽彲鐢憋細(sina)^2+(cosa)^2=1锛屾眰鍑猴細cosa=姝ｈ礋鈭歔(1-(sina)^2]锛涘啀鐢卞崐瑙掑叕寮忥細sin(a/2)=姝ｈ礋鈭歔(1-cosa)/2]锛屾眰鍑簊in(a/2)锛屽啀姹傚嚭a/2銆侾S锛氭眰涓夎鍑芥暟涓瀹氳娉ㄦ剰绗﹀彿锛屽厛鍒ゆ柇瑙掓墍鍦ㄧ殑璞￠檺锛屽畾涓嬩笁瑙掑嚱鏁扮殑绗﹀彿锛屽啀鍒╃敤鐩稿簲鐨勪笁瑙掑叕寮忔眰鍊硷紝鏈鍚庡啀鏍规嵁瑙掓墍鍦ㄨ寖鍥达紝姹傚嚭瑙...
绛旓細sina cosa=鏍瑰彿2,鎵浠ワ紙sina cosa锛夊钩鏂=2锛屽垎瑙ｅ洜寮忥紝寰梥ina骞虫柟 2sinacosa cosa骞虫柟=2銆傚洜涓簊ina骞虫柟 cosa骞虫柟=1锛堝叕寮忥級,鍒sinacosa= 1
绛旓細鍗筹紙sina+cosa锛塣2-2sinacosa=1锛屾墍浠^2-2a=1锛屾晠a=1+鏍瑰彿2鎴1-鏍瑰彿2锛岀敱棰樻剰寰梑^2-4ac澶т簬绛変簬0寰梐澶т簬绛変簬4鎴朼灏忎簬绛変簬0锛屾晠鍙朼=1-鏍瑰彿2銆2.鐢1寰楋紝sinacosa=a=1-鏍瑰彿2锛屽張tana+1/tana=sina/cosa+cosa/sina=锛坰ina^2+cosa^2锛/sinacosa=1/锛1-鏍瑰彿2锛=-鏍瑰彿2-1....
