As tan^2x-6tanx+5=0 is a quadratic equation in tanx, let us first factorize it to find a solution for tanx#.
tan^2x-6tanx+5=0 is equivalent to
tan^2x-tanx-5tanx+5=0
or tanx(tanx-1)-5(tanx-1)-0
or (tanx-5)(tanx-1)=0
i.e. tanx=5 or tanx=1
As tan^(-1)p indicates an angle, say theta, whose tangent is p i.e. tantheta=p
In the given question, we are not to find tanx but x and hence we use definition of inverse function for this and solution of given equation is
x=tan^(-1)1 or x=tan^(-1)5
It is apparent that tan^(-1)1=p/4 but it is not so easy for tan^(-1)5.
To find exact value of x, we need to either look at inverse function tables or use scientific calculator and using this, we get the value of x (in radians as it is an angle) is
x=pi/4=0.7854 or x=1.3734
It is apparent that pi+pi/4=(5pi)/4=3.927 and pi+1.3734=4.515
