JEE Math Practice Question

Let f(x) = loge(sin x), (0 < x < $$\pi $$) and g(x) = sin–1 (e–x ), (x $$ \ge $$ 0). If $$\alpha $$ is a positive real number such that a = (fog)'($$\alpha $$) and b = (fog)($$\alpha $$), then :

1. A.a$$\alpha $$2 + b$$\alpha $$ - a = -2$$\alpha $$2
2. B.a$$\alpha $$2 + b$$\alpha $$ + a = 0
3. C.a$$\alpha $$2 - b$$\alpha $$ - a = 0
4. D.a$$\alpha $$2 - b$$\alpha $$ - a = 1