Question

Question #0ef02

Answer 1

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!

Answer 2

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`