Question #0ef02

2 Answers
Nov 21, 2017

See proof below

Explanation:

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!

Nov 21, 2017

See the explanation below

Explanation:

#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#