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If f(x) is a function given by

f(x)=sinx    sina    sinbcosx    cosa    cosbtanx    tana    tanb,where 0<a<b<π2 Then the equation f(x)=0

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a
has at least one root in (a, b) 
b
 has at most one root in (a, b)
c
 has exactly one root in (a, b)
d
has no root in (a, b)

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detailed solution

Correct option is A

We know that sinx,cosx and tanx are continuous on [a, b] and differentiable on (a, b).

 Therefore,f(x) is continuous on [a, b] and differentiable on (a, b). 

Also, f(a)=f(b)=0

Therefore, by Rolle's theorem there exists at least onec(a,b) such that f(c)=0

Hence, f' (x) = 0 has at least one root in (a, b). 

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