Answer:
first blank box:
cos^2(a)
second blank box:
sin^2(a)
see image.
Explanation:
Usually, to "verify" you work on the equation using algebra and identities...BUT ONLY CHANGING ONE SIDE. Keep the other side the same and try to make them look the same.
The step to get what's in the first blank box is multiplying
(1-cos a)(1+cos a)
which will make a difference of two squares.
The second blank is using a pythagorean identity that
cos^2 + sin^2 = 1
so
1 - cos^2 = sin^2
see image.