If f(x) = sqrt{ cos(sin x)} + sqrt{ sin(cos x)} then range of f(x) is - Maths - Relations and Functions

Question

If f(x) = sqrt{ cos(sin x)} + sqrt{ sin(cos x)} then range of f(x)
is

Ghanshyam Dhakar · Accepted Answer

Dear
student,
fx =cossinx+sincosx 
1for domain ⇒first term is always positive then sincosx≥0 then -π2≤x≤π2 defferentiate eq1f'x = 12cossinx-sinsinx×cosx+12sincosxcoscosx×-sinxf'x =0,then x=0 f0 = 1+sin1f-π2 = fπ2=cos1so fmax = 1+sin1 ,fmin=cos1range  cos1≤fx≤1+sin1
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