Question

please solve this mods/stars‼️

Let f'(sinx)<0 and f "(sinx)>0∀x∈(0, π/2) and g(x)=f(sinx)+f(cosx) ​

Answer 1

Answer:

Correct option is

B

g(x) decreases if x∈(0,4π)

C

g(x) increases if x∈(4π,2π)

g(x)=f(sinx)+f(cosx)

g′(x)=f′(sinx)cosx+f′(cosx)(−sinx)

g′(x)=cosxf′(sinx)−sinxf′(cosx)

g′(x)=cosxf′(sinx)−sinxf′(sin(2π−x))

g′′(x)=−sinxf′(sinx)+cos2xf′′(sinx)−cosxf′(cosx)+sinxf′′(cosx)

f′(sinx)<0 for all x∈(0,2π)

And sinx>0,cosx>