If f(x)=∣∣
∣∣sin xsin asin bcos xcos acos btan xtan atan b∣∣
∣∣,where 0<a<b<π2
then the equation
f′(x)=0 has in the interval (a,b)
Atleast one root
Here f(a)=∣∣
∣∣sin asin asin bcos acos acos btan atan atan b∣∣
∣∣=0.Also f(b)=0.
Moreover, as sin x, cos x and tan x are continuos and differentiable in (a, b) for 0 < a < b < π2, therefore f(x) is also continuos and differentiable in [a, b]. Hence, by Rolle's theorem, there exists atleast one real number c in (a, b) such that f ' (c) = 0.
Hence (a) is the correct answer.