Question

find general solution tan2x =tan2/x

Answer 1

Answer:

Questions:-

$\rm\tan2x = \tan \dfrac{2}{x}$

To find :-

General solution

Solution:-

$\rm\tan2x = \tan \dfrac{2}{x}$

We know the property that trigonometric equation have general solution ..

when

$\rm \: \tan \theta \: = \tan \alpha$

then,

$\rm \theta = \: n\pi + \alpha$

so, using it in the given equation

$\implies \rm \: 2x = n\pi + \dfrac{2}{x}$

$\implies \rm \: 2x - n\pi - \dfrac{2}{x} = 0$

$\rm \implies \dfrac{2 {x}^{2} - n\pi x - 2 }{x} = 0$

$\rm \implies {2 {x}^{2} - n\pi x - 2 } = 0$

Here a = 2 , b = -nπ c = -2

$\implies \rm \: x = \dfrac{ -( -n\pi) \pm \: \sqrt{ {(n\pi)}^{2} + 4.2.2 } }{2.2}$

$\underline{\boxed{\implies \rm x = \dfrac{n\pi \pm \sqrt{ {n}^{2} {p}^{2} + 16 } }{4} }}$Hense, This is the required general solution.

Note :- Attached picture ( All general solution of trigonometric equation )

Answer 2

kya yaar itne easy questions hain....