Using the relation $2 ( 1 - \cos x ) < x ^ { 2 } , x ^ { 1 } 0$ or otherwise, prove that $\sin ( \tan x ) > x \forall x \hat { \mathrm { I } } [ 0 , \pi / 4 ]$.
The minimum value of $f ( x ) = x ^ { 2 } + 2 b x + 2 c ^ { 2 }$ is more than the maximum value of $g ( x ) = - x ^ { 2 } - 2 c x + b ^ { 2 } , x$ being real, for
Using the relation $2 ( 1 - \cos x ) < x ^ { 2 } , x ^ { 1 } 0$ or otherwise, prove that $\sin ( \tan x ) > x \forall x \hat { \mathrm { I } } [ 0 , \pi / 4 ]$.