Question

cos 20 - sin 20 greater than 0​

Answer 1

SOLUTION

Mate, Happy Independence Day and here is you solution .If you don't understand anything you are free to ask me.

$</p><p><strong><u>To</u></strong><strong><u>\</u></strong><strong><u>:</u></strong><strong><u>Prove</u></strong><strong><u>:</u></strong><strong><u>\</u></strong><strong><u>:</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>cos</u></strong><strong><u> </u></strong><strong><u>2</u></strong><strong><u>\</u></strong><strong><u>theta</u></strong><strong><u> </u></strong><strong><u>-</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>sin</u></strong><strong><u> </u></strong><strong><u>2</u></strong><strong><u>\</u></strong><strong><u>theta</u></strong><strong><u>></u></strong><strong><u>0</u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u> </u></strong><strong><u>Proof</u></strong><strong><u>\</u></strong><strong><u>\</u></strong></p><p><strong>W</strong><strong>e</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>can</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>write</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>\</strong><strong>sin</strong><strong> </strong><strong>2</strong><strong>\</strong><strong>theta</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>as</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>\</strong><strong>sin</strong><strong>(</strong><strong>\</strong><strong>theta</strong><strong>+</strong><strong>\</strong><strong>theta</strong><strong>)</strong><strong>\</strong><strong>\</strong></p><p><strong>By</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>using</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>the</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>sin</strong><strong>(</strong><strong>a</strong><strong>+</strong><strong>b</strong><strong>)</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>identity</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>we</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>will</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>get</strong><strong>,</strong><strong>\</strong><strong>\</strong></p><p><strong>2</strong><strong>\</strong><strong>cos</strong><strong> </strong><strong>\</strong><strong>theta</strong><strong>\</strong><strong>\</strong></p><p><strong>Similarly</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>we</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>can</strong><strong>\</strong><strong>:</strong><strong>write</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>cos</strong><strong> </strong><strong>2</strong><strong>\</strong><strong>theta</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>as</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>cos</strong><strong>(</strong><strong>\</strong><strong>theta</strong><strong>+</strong><strong>\</strong><strong>theta</strong><strong>)</strong><strong>\</strong><strong>:</strong><strong>and</strong><strong>\</strong><strong>:</strong><strong>get</strong><strong>\</strong><strong>:</strong><strong>2</strong><strong>\</strong><strong>cos</strong><strong> </strong><strong>\</strong><strong>theta</strong><strong>\</strong><strong>\</strong></p><p><strong>Now</strong><strong> </strong><strong>,</strong><strong>\</strong><strong>\</strong></p><p><strong>By</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>substituting</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>values</strong><strong>,</strong><strong>\</strong><strong>\</strong><strong>We</strong><strong>\</strong><strong>:</strong><strong>get</strong><strong>,</strong><strong>\</strong><strong>\</strong></p><p><strong>4</strong><strong>(</strong><strong>\</strong><strong>cos</strong><strong>\</strong><strong>theta</strong><strong>)</strong><strong>></strong><strong>0</strong><strong>\</strong><strong>\</strong></p><p><strong>=</strong><strong>></strong><strong>4</strong><strong>></strong><strong>0</strong><strong>\</strong><strong>\</strong></p><p><strong>Since</strong><strong>,</strong><strong>4</strong><strong>></strong><strong>0</strong><strong>\</strong><strong>\</strong></p><p><strong>Therefore</strong><strong>,</strong><strong>\</strong><strong>\</strong></p><p><strong>\</strong><strong>cos</strong><strong> </strong><strong>2</strong><strong>\</strong><strong>theta-</strong><strong> </strong><strong>\</strong><strong>sin</strong><strong> </strong><strong>2</strong><strong>\</strong><strong>theta</strong><strong>\</strong><strong>:</strong><strong>is</strong><strong>\</strong><strong>:</strong><strong>also</strong><strong>\</strong><strong>:</strong><strong>greater</strong><strong>\</strong><strong>:</strong><strong>than</strong><strong>\</strong><strong>:</strong><strong>0</strong><strong>\</strong><strong>:</strong><strong>in</strong><strong>\</strong><strong>:</strong><strong>any</strong><strong>\</strong><strong>:</strong><strong>values</strong><strong>\</strong><strong>:</strong><strong>of</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>\</strong><strong> </strong><strong>\</strong><strong>theta</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>excluding</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\</strong><strong>theta</strong><strong>=</strong><strong>9</strong><strong>0</strong><strong>°</strong><strong>\</strong><strong>\</strong><strong> </strong><strong> </strong><strong>Because</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>the</strong><strong>\</strong><strong>:</strong><strong>answer</strong><strong>\</strong><strong>:</strong><strong>would</strong><strong>\</strong><strong>:</strong><strong>be</strong><strong>\</strong><strong>:</strong><strong>equal</strong><strong>\</strong><strong>:</strong><strong>to</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>0</strong></p><p>$

Answer 2

Answer:

cos20=0.408082062

sin20=0.912945251

Step-by-step explanation:

cos 20 - sin 20=0.504663189