Question # XI. Solve the following equations:-
(1) tan (cos-?x) = sin(tan-12)
(2) tan-11*
tan-x
x>0
(3) 2 tan-(sin x) = tan-(2 sec x) 0

# XI. Solve the following equations:-
(1) tan (cos-?x) = sin(tan-12)
(2) tan-11*
tan-x
x>0
(3) 2 tan-(sin x) = tan-(2 sec x) 0

Solution ( theta ) only one in one time
(?) ( tan ^{1} frac{1-x}{1+x}=frac{1}{2} pi n^{-1} x )
( operatorname{PTan} 1left(frac{1-x}{1+x}right)=operatorname{Tan} 1 x )
( left.tan ^{-1} frac{left(frac{2-2 x}{1+x}right.}{1-left(frac{1-x}{1+x}right)^{2}}right)=tan x )
( Pleft(frac{1-x}{1+x}right)=2left(1+x^{2}+2 x-right. )
( left(frac{1-x}{1+x}right)=frac{4 x^{2}}{(1+x)} )
( 1+x=0 )
( 12 x=-1 )
[
begin{array}{c}
Pleft(1-x^{2}right)=4 x^{2}
2-2 x^{2}=4 x^{2}
x=6 x^{2}
end{array}
]
( int_{2}^{2}=frac{frac{1}{3}}{sqrt{3}} )

Solution