This equation is not correct. Let's simplify both sides of the equation to verify:

Starting with the left side:
sin^4(a) + cos^4(a)

Using the trigonometric identity sin^2(a) + cos^2(a) = 1, we can rewrite this expression as:

(sin^2(a) + cos^2(a))^2 - 2sin^2(a)cos^2(a)
= 1^2 - 2sin^2(a)cos^2(a)
= 1 - 2sin^2(a)cos^2(a)

Therefore, the left side should be:
1 - 2sin^2(a)cos^2(a)

Now, let's simplify the right side:
1 - 0.5sin^2(2a)
= 1 - 0.5(2sin(a)cos(a))^2
= 1 - 0.5(4sin^2(a)cos^2(a))
= 1 - 2sin^2(a)cos^2(a)

So, after simplification, the right side is equal to the left side.
Therefore, the given equation is correct:

sin^4(a) + cos^4(a) = 1 - 0.5sin^2(2a)