For x [ ] (0, 3/2), let f(x) = [ x ] , g(x) = tan x and h(x) = [1 - x^2 1 + x^2].

Question

For x $$ \in $$ (0, 3/2), let f(x) = $$\sqrt x $$ , g(x) = tan x and h(x) = $${{1 - {x^2}} \over {1 + {x^2}}}$$. If $$\phi $$ (x) =  ((hof)og)(x),  then $$\phi \left( {{\pi  \over 3}} \right)$$
 is equal to :

Accepted Answer

$$\phi \left( x \right) = \left( {\left( {hof} \right)og} \right)(x) = h\left( {\sqrt {\tan x} } \right)$$

$$ \Rightarrow \phi (x) = {{1 - \tan x} \over {1 + \tan x}} = \tan \left( {{\pi  \over 4} - 4} \right)$$

$$ \therefore $$ $$\phi \left( {{\pi  \over 3}} \right) = \tan \left( {{\pi  \over 4} - {\pi  \over 3}} \right)$$

$$ \Rightarrow \tan \left( { - {\pi  \over {12}}} \right) = \tan {{11\pi } \over {12}}$$

Solutions · 1