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Question:

For x∈(0, 3/2), let f(x)=√x, g(x)=tan x and h(x)=(1-x²)/(1+x²). If φ(x)=((hof)og)(x), then φ(π/3) is equal to?

tan 7π/12

tan 11π/12

tan 5π/12

tan π/12

Solution:

Correct option is C. tan 11π/12
f(x)=√x, g(x)=tan x, h(x)=(1-x²)/(1+x²)
f(g(x))=tan x
h(f(g(x)))=h(tan x)=(1-tan²x)/(1+tan²x)=tan(π/4-x)
φ(x)=tan(π/4-x)
φ(π/3)=tan(π/4-π/3)=tan(-π/12)=-tan(π/12)=tan(π-π/12)=tan(11π/12).