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#1
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⨷Âì Trigonometry ÂÒ¡ªèÇÂá¹Ð¹ÓÇԸդԴ˹èͤÃѺ
⨷ÂìµÒÁ Link ¹Õé¤ÃѺ
á¡éä´éáÅéǤÃѺ à»ç¹á¹Ç¢éÍÊͺ¡ÅÒ§ÀÒ¤àµÃÕÂÁÍØ´Á 15 ¡Ã¡®Ò¤Á 2016 16:07 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 8 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ Wutirat à˵ؼÅ: pic |
#2
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á¡éä¢â¨·Âì¢éÍ 1 ãËÁè
á¡éä¢â¨·Âì¢éÍ 1 ãËÁè
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#3
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ÍéÒ§ÍÔ§:
1) ¨Ñº¤Ùè´Õæ¤ÃѺ à´ÕëÂǨШѴÃÙ»ä´é¹Ô¾¨¹ì·ÕèÁÕ $tan 36,tan 72 $ â¼Åè¢Öé¹ÁÒ¤ÃѺ 2) ÁØÁÊÒÁà·èÒ 3) A = Êٵüźǡ-źÁØÁ B= ·ÓµÒÁ¤Ùè·ÕèÁÕ¤ÃѺ ¤ÙèËÅѧ¡çà»ÅÕè¹ $cot$ ¡Ñº $tan$ à»ç¹ÁØÁÊͧà·èÒãËéä´é¤ÃѺ 4) ¨Ñ´ÃÙ»¡ÓÅѧÊͧÊÁºÙóì + ÊٵüźǡźÁØÁ 15 ¡Ã¡®Ò¤Á 2016 20:55 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¿Ô¹Ô¡«ìàËÔ¹¿éÒ à˵ؼÅ: à¾ÔèÁ 3B |
#4
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¢éÍ4)
$\frac{tanA}{1-tan^{2}A}=sin^{2}20^{\circ}-sin160^{\circ }sin220^{\circ }+sin^{2}320^{\circ } $ $\frac{tan2A}{2}= sin^{2}20^{\circ}+sin20^{\circ }sin40^{\circ }+sin^{2}40^{\circ } $ $tan2A=2sin^{2}20^{\circ}+2sin20^{\circ }sin40^{\circ }+2sin^{2}40^{\circ } $ $tan2A=1-cos40^{\circ }+cos20^{\circ }-cos60^{\circ }+1-cos80^{\circ }$ $tan2A=\frac{3}{2} +cos20^{\circ }-cos40^{\circ }-cos80^{\circ }$ $tan2A=\frac{3}{2}+2sin30^{\circ }sin10^{\circ }-sin10^{\circ }$ $\therefore tan2A=\frac{3}{2}$ áÅШҡÊٵà $tan3\theta =\frac{3tan\theta -tan^{3}\theta }{1-3tan^{2}\theta } $ ¨Ðä´éÇèÒ .............. $tan6A=\frac{3tan2A -tan^{3}2A}{1-3tan^{2}2A } $ $tan6A=\frac{(3)(\frac{3}{2}) -(\frac{3}{2})^{3} }{1-(3)(\frac{3}{2})^{2} } $ $tan6A=\frac{\frac{9}{2} -\frac{27}{8} }{1-\frac{27}{4} } $ $tan6A=-\frac{9}{46} $ |
#5
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3)
$A=\frac{1}{sin20^{\circ }cos40^{\circ }} +\frac{1}{\sqrt{3} cos20^{\circ }cos40^{\circ }}$ $A=\frac{2cos20^{\circ }}{2cos20^{\circ }sin20^{\circ }cos40^{\circ }}+\frac{2sin20^{\circ }}{(\sqrt{3})2 sin20^{\circ }cos20^{\circ }cos40^{\circ }}$ $A=\frac{2cos20^{\circ }}{sin40^{\circ }cos40^{\circ }}+\frac{2sin20^{\circ }}{(\sqrt{3}) sin40^{\circ }cos40^{\circ }}$ $A=\frac{4cos20^{\circ }}{sin80^{\circ }}+\frac{4sin20^{\circ }}{\sqrt{3} sin80^{\circ }}$ $A=\frac{4\sqrt{3}cos20^{\circ }+4sin20^{\circ } }{\sqrt{3} sin80^{\circ }} $ $A=\frac{8(\frac{\sqrt{3} }{2}cos20^{\circ }+\frac{1}{2}sin20^{\circ }) }{\sqrt{3} sin80^{\circ }} $ $A=\frac{8(cos30^{\circ }cos20^{\circ }+sin30^{\circ }sin20^{\circ })}{\sqrt{3} sin80^{\circ }} $ $A=\frac{8cos10^{\circ }}{\sqrt{3} sin80^{\circ }} $ $A=\frac{8cos10^{\circ }}{\sqrt{3} cos10^{\circ }} $ $A=\frac{8}{\sqrt{3} } $ ------------------------------------------------------------------------------- $B=cot40^{\circ }+cot230^{\circ }-tan185^{\circ }(tan230^{\circ }-cot50^{\circ })$ $B=cot40^{\circ }+tan40^{\circ }-tan5^{\circ }(cot40^{\circ }-cot50^{\circ })$ $B=\frac{cos40^{\circ }}{sin40^{\circ }} +\frac{sin40^{\circ }}{cos40^{\circ }}-tan5^{\circ }(\frac{cos40^{\circ }}{sin40^{\circ }} -\frac{cos50^{\circ }}{sin50^{\circ }})$ $B=\frac{cos^{2}40^{\circ }+sin^{2}40^{\circ }}{sin40^{\circ }cos40^{\circ }} -tan5^{\circ }(\frac{sin50^{\circ }cos40^{\circ }-cos50^{\circ }sin40^{\circ }}{sin40^{\circ }sin50^{\circ }}) $ $B=\frac{2}{sin80^{\circ }}-tan5^{\circ }(\frac{sin10^{\circ }}{sin40^{\circ }cos40^{\circ }} )$ $B=\frac{2}{sin80^{\circ }}-tan5^{\circ }(\frac{2sin10^{\circ }}{sin80^{\circ }}) $ $B=\frac{2}{cos10^{\circ }}-\frac{sin5^{\circ }}{cos5^{\circ }}(\frac{2sin10^{\circ }}{cos10^{\circ }}) $ $B=\frac{2}{cos10^{\circ }}\left(1-sin10^{\circ }\frac{sin5^{\circ }}{cos5^{\circ }} \right) $ $B=\frac{2}{cos10^{\circ }}\left(1-2sin5^{\circ }cos5^{\circ }\frac{sin5^{\circ }}{cos5^{\circ }} \right) $ $B=\frac{2}{cos10^{\circ }}\left(1-2sin^{2}5^{\circ }\right) $ $B=\frac{2}{cos10^{\circ }}\left(cos10^{\circ }\right) $ $B=2$ ----------------------------------------------------------------------- $AB=(\frac{8}{\sqrt{3} } )(2)$ $AB=\frac{16}{\sqrt{3} } $ |
#6
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2)
$\frac{12tan^{2}A-4tan^{4}A}{6tanA-18tan^{3}A} =36cos^{2}10^{\circ }-96sin^{4}80^{\circ }+64cos^{6}370^{\circ }$ $\frac{(4tanA)(3tanA-tan^{3}A)}{(6tanA)(1-3tan^{2}A)} =36cos^{2}10^{\circ }-96cos^{4}10^{\circ }+64cos^{6}10^{\circ }$ $\left(\frac{2}{3} \right) (tan3A)=18(2cos^{2}10^{\circ })-24(2cos^{2}10^{\circ })^{2}+8(2cos^{2}10^{\circ })^{3}$ $\left(\frac{2}{3} \right) (tan3A)=18(cos20^{\circ }+1)-24(cos20^{\circ }+1)^{2}+8(cos20^{\circ }+1)^{3}$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(18-24(cos20^{\circ }+1)+8(cos20^{\circ }+1)^{2})$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(18-(cos20^{\circ }+1)(24-8(cos20^{\circ }+1)))$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(18-(cos20^{\circ }+1)(16-8cos20^{\circ }))$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(18-16-8cos20^{\circ }+8cos^{2}20^{\circ })$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(2-8cos20^{\circ }+4(cos40^{\circ }+1))$ $\left(\frac{2}{3} \right) (tan3A)=(cos20^{\circ }+1)(6-8cos20^{\circ }+4cos40^{\circ })$ $\left(\frac{2}{3} \right) (tan3A)=6cos20^{\circ }-8cos^{2}20^{\circ }+4cos40^{\circ }cos20^{\circ }+6-8cos20^{\circ }+4cos40^{\circ }$ $\left(\frac{2}{3} \right) (tan3A)=6cos20^{\circ }-4(cos40^{\circ }+1)+2(cos60^{\circ }+cos20^{\circ })+6-8cos20^{\circ }+4cos40^{\circ }$ $\left(\frac{2}{3} \right) (tan3A)=3+8cos20^{\circ }-4cos40^{\circ }-8cos20^{\circ }+4cos40^{\circ }$ $\left(\frac{2}{3} \right) (tan3A)=3$ $\therefore tan3A=\frac{9}{2} $ $\Rightarrow sin3A=\frac{9}{\sqrt{85} } ..........(5^{\circ} <A<30^{\circ })$ |
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