Need help with 2 trigonometry questions

Simplify to a trigonometric function of a single angle. Then give the exact value if possible.

1.) cos20cos40 - sin20sin40

2.) sin130 cos80 + cos130 sin80

Any work/ explaination would be much appreciated. Thank you! :)

1) cos20cos40 - sin20sin40 = cos (20 + 40) = cos 60 = 0.5

2) sin130cos80 + cos130sin80 = sin (130 + 80) = sin 210 = sin(180+30) = -sin30 = -root(3)/2

Recall the trig identity for the cos of a sum
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
So here
cos20cos40 - sin20sin40 = cos(20+40) = cos(60) = 0.5

For the second one, it is the sin of the sum of two angles:
sin(a + b) = sin(a)cos(b) + sin(b)cos(a)
So here
sin(130)cos(80) + sin(80)cos(130) = sin(130+80) = sin(210) = -0.5

1.) cos20cos40 - sin20sin40
= cos (20+40) ////// cos (a+b) = cos a cos b - sin a sin b
= cos 60
= 1/2

2.) sin130 cos80 + cos130 sin80
= sin ( 180 -50) cos 80 + cos ( 180 - 50) sin 80
= sin 50 cos 80 - cos 50 sin 80 /// sin (x-y) = sin x cos y - sin y cos x
= sin (50 -80)
= sin (-80)
= - sin 80