How can I check if the period of a trigonometric equation solution is #npi" or "2npi# ?
#(sinx+cosx)*sqrt(2)=tanx+cotx#
Solving this equation I got x= #pi/4+npi# , but my professor said the solution should be x= #pi/4+2npi#
How is this checked?
Solving this equation I got x=
How is this checked?
1 Answer
See the explanation, and graph for verification.
Explanation:
The least positive P for which f (x + P) = f (x ) is the period of f( x ).
The period for both sin x and cos x is
The period for both tan x and cot x is
The LCM is
So, this is the overall period for
You can verify that
So, the general solution is
Graph reveals this.
graph{y - sqrt 2 (sin x + cos x )+tan x + cot x = 0[-20 20 -10 10]}
The graph braces x-axis, for the solutions, at
respectively, as approximations.