If `f(x) =|(sinx,sin a,sin b),(cos x,cosa,cosb),(tanx,tana,tanb)|`,where `0 < alt blt pi/2`, then the equaltion `f'(x)=0` has,in the interval `(a,b)`

If f(x) = |{:(sinx,sina, sin b),(cos x , cos a, cos b),(tanx,tana,tanb):}| ,where 0 lt a lt b lt ( pi )/(2) , then the equation f'(x) = 0 has, in the interval (a,b)

If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,cosa,cosb),(tan x , tan a, tan b):}|" where"0 lt altblt(pi)/(2) Then the equatiion f'(x)=0

If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,cosa,cosb),(tan x , tan a, tan b):}|" where"0 lt altblt(pi)/(2) Then the equatiion f'(x)=0

Let 0ltaltblt(pi)/(2).Iff(x)= |{:(tanx,tana, tanb),(sinx,sina,sinb),(cosx,cosa,cosb):}|,then find the minimum possible number of roots of f'(x) = 0 in (a,b).

Let 0ltaltbltpi/2. \ If \ f(x)=|[tanx,tana,tanb],[sinx,sina,sinb],[cosx,cosa,cosb]| , then find the minimum possible number of roots of f^(prime)(x)=0 in (a , b) .

Let 0ltaltbltpi/2. \ If \ f(x)=|[tanx,tana,tanb],[sinx,sina,sinb],[cosx,cosa,cosb]| , then find the minimum possible number of roots of f^(prime)(x)=0 in (a , b)

Let 0ltaltbltpi/2. \ If \ f(x)=|[tanx,tana,tanb],[sinx,sina,sinb],[cosx,cosa,cosb]| , then find the minimum possible number of roots of f^(prime)(x)=0 in (a , b) .

Prove that (sin5x-2sin3x+sinx)/(cos5x-cosx)=tanx

Prove that =(sin 5x-2sin3x+sinx)/(cos5x-cosx)=tanx