cos2acos2b + sqr(sin(a-b)) - sqr(sin(a+b)) = ?
To simplify the given expression cos^2(a)cos^2(b) + (√(sin(a-b)))^2 - (√(sin(a+b)))^2, we can use some trigonometric identities.
Let's start with the first term, cos^2(a)cos^2(b). We know that cos^2(x) = 1 - sin^2(x), so we can rewrite cos^2(a)cos^2(b) as (1 - sin^2(a))(1 - sin^2(b)).
Now, let's simplify the second term, (√(sin(a-b)))^2 = sin(a-b).
The third term, (√(sin(a+b)))^2 = sin(a+b).
Now, let's substitute these expressions back into the original equation:
(1 - sin^2(a))(1 - sin^2(b)) + sin(a-b) - sin(a+b)
Expanding the first term using the distributive property:
(1 - sin^2(a))(1 - sin^2(b)) = 1 - sin^2(a) - sin^2(b) + sin^2(a)sin^2(b)
Now let's combine like terms:
1 - sin^2(a) - sin^2(b) + sin^2(a)sin^2(b) + sin(a-b) - sin(a+b)
There are no more simplifications we can make, so this is the simplified form of the given expression:
1 - sin^2(a) - sin^2(b) + sin^2(a)sin^2(b) + sin(a-b) - sin(a+b)