Answer:
Explanation:
We can start by combining the two fractions by finding a common denominator:
sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)
= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))
= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2
= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))
= (2 + 2cos(a)) / (sin(a) + cos(a))^2
= 2(1+cos(a)) / (sin(a) + cos(a))^2
= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)
= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2
This expression cannot be simplified further without additional information or context.