Question

the general solution of cot 2x=1 is

Answer 1

Cot2x = 1
Cot2x = cotπ/4
Do you one thing about general solution of Trigonometric function ?
Solution may be more than one. Cause trigonometry functions are periodic functions.

Now, if cotФ = cotα then, Ф = nπ + α where n ∈ $\mathbb{Z}$
So, cot2x = cotπ/4
It means, 2x = nπ + π/4
Or, x = nπ/2 + π/8 , where n ∈ $\mathbb{Z}$

Answer 2

Solution:-

given by:-
$Cot2x = 1 \\ Cot2x = cotπ/4 \\ Now, if \: cot \theta = cotα \: \\ then, \theta= nπ + α \\ where \: \: n ∈ Z \\ So, \\ cot2x = cotπ/4 \\ It means, \\ 2x = nπ + π/4 \\ Or, \\ x = nπ/2 + π/8 \\ , where \: \: n ∈ Z$
●GENRAL SOLUTION:- solution of an ordinary differential equation of order n that involves exactly n essential arbitrary constants — called also complete solution, general integral. 2 : a solution of a partial differential equation that involves arbitrary functions — called also general integral.


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