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Overleg:John Napier: verschil tussen versies

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(10 tussenliggende versies door dezelfde gebruiker niet weergegeven)
Regel 1: Regel 1:
test
(1)
<span class="_nowrap" style="white-space:nowrap;" {{#if:|>tan {{Vbreuk|A + B|2}}<span style="display:none">&nbsp;</span><span}} <!--
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;tan {{Vbreuk|A + B|2}}&nbsp;<!--
-->style="display:inline-block; vertical-align:-0.5em; font-size:100%; text-align:center;"><!--
   --><span style="display:block; border-top:1px solid;">tan {{Vbreuk|C|2}} </span></span> =
  --><span style="display:block; line-height:1em; padding:0 0.1em;">{{#if:|&nbsp;tan {{Vbreuk|C|2}} &nbsp;|{{#if:tan {{Vbreuk|C|2}} |&nbsp;tan {{Vbreuk|A + B|2}}&nbsp;|&nbsp;1&nbsp;}}}}</span><!--
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;cos {{Vbreuk|A − B|2}}&nbsp;<!--
  --><span style="display:none">/</span><!--
   --><span style="display:block; border-top:1px solid;">cos {{Vbreuk|A + B|2}} </span></span>
   --><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">tan {{Vbreuk|C|2}} </span><!--
-->{{#if:|</span>}}<!--
--></span> = <span class="_nowrap" style="white-space:nowrap;" {{#if:|>cos {{Vbreuk|A - B|2}}<span style="display:none">&nbsp;</span><span}} <!--
-->style="display:inline-block; vertical-align:-0.5em; font-size:100%; text-align:center;"><!--
  --><span style="display:block; line-height:1em; padding:0 0.1em;">{{#if:|&nbsp;cos {{Vbreuk|A + B|2}} &nbsp;|{{#if:cos {{Vbreuk|A + B|2}} |&nbsp;cos {{Vbreuk|A - B|2}}&nbsp;|&nbsp;1&nbsp;}}}}</span><!--
  --><span style="display:none">/</span><!--
   --><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">cos {{Vbreuk|A + B|2}} </span><!--
-->{{#if:|</span>}}<!--
--></span>  


(2)
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;tan {{Vbreuk|a − b|2}}&nbsp;<!--
  --><span style="display:block; border-top:1px solid;">tan {{Vbreuk|C|2}} </span></span> =
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;sin {{Vbreuk|A − B|2}}&nbsp;<!--
  --><span style="display:block; border-top:1px solid;">sin {{Vbreuk|A + B|2}} </span></span>


<span style="font-size: 18px;">
(3)
    <span style="display: inline-block; text-align: center; vertical-align: middle;">
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;tan {{Vbreuk|A + B|2}}&nbsp;<!--
        <span style="display: inline-block; text-align: center; width: 100%; margin-top: -5px;">
  --><span style="display:block; border-top:1px solid;">cot {{Vbreuk|C|2}} </span></span> =
            <span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">tan</span>
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;cos {{Vbreuk|a − b|2}}&nbsp;<!--
            (<span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">(A + B)/2</span>)
  --><span style="display:block; border-top:1px solid;">cos {{Vbreuk|a + b|2}} </span></span>
        </span>
 
        <span style="display: block; text-align: center;">/</span>
(4)
        <span style="display: inline-block; text-align: center; width: 100%; margin-top: -5px;">
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;tan {{Vbreuk|A − B|2}}&nbsp;<!--
            <span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">tan</span>
  --><span style="display:block; border-top:1px solid;">cot {{Vbreuk|C|2}} </span></span> =
            (<span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">(C/2)</span>)
<span style="display:inline-block; vertical-align:-1em; text-align:center;">&nbsp;sin {{Vbreuk|a − b|2}}&nbsp;<!--
        </span>
  --><span style="display:block; border-top:1px solid;">sin {{Vbreuk|a + b|2}} </span></span>
    </span>
    <span style="display: inline-block; text-align: center; vertical-align: middle; margin: 0 10px;">=</span>
    <span style="display: inline-block; text-align: center; vertical-align: middle;">
        <span style="display: inline-block; text-align: center; width: 100%; margin-top: -5px;">
            <span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">cos</span>
            (<span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">(A - B)/2</span>)
        </span>
        <span style="display: block; text-align: center;">/</span>
        <span style="display: inline-block; text-align: center; width: 100%; margin-top: -5px;">
            <span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">cos</span>
            (<span style="font-family: 'Times New Roman', Times, serif; font-weight: bold; font-style: italic;">(A + B)/2</span>)
        </span>
    </span>
</span>

Huidige versie van 8 nov 2023 om 06:49

(1)  tan  A + B /2 tan  C /2 =  cos  A − B /2 cos  A + B /2

(2)  tan  a − b /2 tan  C /2 =  sin  A − B /2 sin  A + B /2

(3)  tan  A + B /2 cot  C /2 =  cos  a − b /2 cos  a + b /2

(4)  tan  A − B /2 cot  C /2 =  sin  a − b /2 sin  a + b /2

Overgenomen van "https://nl.wikisage.org/w/index.php?title=Overleg:John_Napier&oldid=355465"