The set of all real values of λ for which the function f(x)=1-cos2x·(λ+sinx),x∈-π2,π2, has exactly one maxima and exactly one minima, is:

f(x)=1-Cos2x(λ+sinx)  =Sin2x(λ+sinx)f1(x)=sin2xCosx+(λ+sinx)2sinxcosx=sinxcosx(2λ+3sinx)For maximum or minimum,f1(x)=0  ⇒sinx=0 or sinx=-2λ3 As there is exactly one max. and exactly one min, f'(x)=0 has exactly 2 roots -1<2λ3<1 and -2λ3≠0  ⇒λ∈-32,32-{0}