If `Det[[1,sinx,sin^2x],[1,cosx,cos^2x],[1,tanx,tan^2x]]=0`, `x in [0,2pi]`, then number of possible values of x is

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Let f(x)=[(sin^2x,sinx,1),(sinx,1,sin^2x),(1,sin^2x,sinx)] and g(x)=[(cos^2x,cosx,1),(cosx,1,cos^2x),(1,cos^2x,cosx)]. If h(x)=Tr.(f(x)g(x)), then find the absolute value of the difference between maximum and minimum value of h(x). [Tr. (P) denotes the trace of Matrix P]

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

If log_(sinx)(cos x) = (1)/(2) , where x in (0, (pi)/(2)) , then the value of sin x is equal to-

(sinx+cosx)/(sinx-cos x)-(sec^(2)x+2)/(tan^(2)x-1)= , where x in (0, (pi)/(2))

(sinx+cosx)/(sinx-cos x)-(sec^(2)x+2)/(tan^(2)x-1)= , where x in (0, (pi)/(2))

If ((1+cos2x))/(sin2x)+3(1+(tanx)tan.(x)/(2))sin x=4 then the value of tanx can be equal to

If ((1+cos2x))/(sin2x)+3(1+(tanx)tan.(x)/(2))sin x=4 then the value of tanx can be equal to