Question #0ef02

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Answer 1 · 2017-11-21T18:53:38

See proof below

Let's first translate all these angles to angles between 0 and 360 degrees:

$cos 510 * cos 330 + sin 390 * cos 120$

$cos (510-360) * cos 330 + sin (390-360) * cos 120$

$cos 150 * cos 330 + sin 30 *cos 120$

Now, we can translate all these angles to angles between 0 and 90 degrees. Remember that some will turn negative:

$-cos 30 * cos 30 + sin 30 * (-cos 60)$

Finally, we can find the exact values:

$-sqrt3/2 * sqrt3/2 + 1/2 * (-1/2)$

$-3/4-1/4$

$-1$

If you need me to explain more (why some values turn negative, etc.), just comment! Hope this helps!

Answer 2 · 2017-11-21T19:02:58

See the explanation below

$cos(510)=cos(510-360)=cos(150)=-cos30=-sqrt3/2$

$cos(330)=cos(-30)=cos(30)=sqrt3/2$

$cos(510)*cos(330)=-sqrt3/2*sqrt3/2=-3/4$

$sin(390)=sin(360+30)=sin30=1/2$

$cos120=-cos60=-1/2$

$sin(390)*cos(120)=1/2*-1/2=-1/4$

Therefore,

$cos(510)*cos(330)+sin(390)*cos(120)=-3/4-1/4=-1$

$QED$