Question

If f(x)=2x.sqroot(1-x^2),then show that f(sin x/2)=sin x

Answer 1

Answer:

f(x)=

1+x

2

2x

now, f(tanθ)=

1+tan

2

θ

2tanθ

=

sec

2

θ

2tanθ

∴ f(tanθ)=2

cosθ

sinθ

×cos

2

θ

=2sinθcosθ

f(tanθ)=sin2θ