First, let's simplify each individual term:
Now, we can substitute these simplified terms back into the expression:
cos^2(a) - ctg^2(a) / tg^2(a) - sin^2(a= (1 - sin^2(a)) - (1/tan(a))^2 / tan^2(a) - sin^2(a= 1 - sin^2(a) - 1/tan^2(a) / tan^2(a) - sin^2(a= 1 - sin^2(a) - cos^2(a) / tan^2(a) - sin^2(a= 1 - sin^2(a) - (1 - sin^2(a)) / tan^2(a) - sin^2(a= 1 - sin^2(a) - 1 + sin^2(a) / tan^2(a) - sin^2(a= 0 / tan^2(a) - sin^2(a= 0 - sin^2(a= -sin^2(a)
Therefore, the simplified expression is equal to -sin^2(a).
First, let's simplify each individual term:
cos^2(a) = 1 - sin^2(a) by the Pythagorean identity for cosine and sine.ctg(a) = 1/tan(a) by the reciprocal identity for cotangent and tangent.Now, we can substitute these simplified terms back into the expression:
cos^2(a) - ctg^2(a) / tg^2(a) - sin^2(a
= (1 - sin^2(a)) - (1/tan(a))^2 / tan^2(a) - sin^2(a
= 1 - sin^2(a) - 1/tan^2(a) / tan^2(a) - sin^2(a
= 1 - sin^2(a) - cos^2(a) / tan^2(a) - sin^2(a
= 1 - sin^2(a) - (1 - sin^2(a)) / tan^2(a) - sin^2(a
= 1 - sin^2(a) - 1 + sin^2(a) / tan^2(a) - sin^2(a
= 0 / tan^2(a) - sin^2(a
= 0 - sin^2(a
= -sin^2(a)
Therefore, the simplified expression is equal to -sin^2(a).