Tan theta= cot(10 degrees +5theta)

Question

Find one angle theta that satisfies tan theta = cot(10 degrees + 5 theta)

Answer 1

 

tan T = cot(5T+10)

 

tan T = 1/tan(5T+10)

 

tan T * tan(5T+10) = 1

 

So 0 = tan T * tan(5T+10) - 1 = f(T) is a function of T  

 

and it is highly discountinuous

 

A little bit of bisection method and looking at the graph there are infinitely

many solutions.

 

For example, there is one solution between

10.637 and 10.638

because f(10.637) <0 while f(10.638)>0