Use the sum-to-product formulas to find the exact value of the following expression:?

Question

cos 120°+cos 30°
Could somebody please show me how to work this problem?

Answer 1

cos(120)+cos(30)= 2*cos(2(120+30))*cos(2(120-30))
=2cos(300)*cos(180)=2*(1/2)*(-1)=-1

Answer 2

Where are you stuck? Go look up the sum-to-product formula for adding two sines: it will look something like:

sin a + sin b = sin((a+b)/2) cos ((a-b)/2)

Plug in your values of 150 and 30. Do the math for your two new angles. They'll be angles for which you already know the sine and cosine -- you may have to apply the identities, such as finding cos(180-30) from sin(30).

Plug in those sine and cosine values, do the math, and you're done.