Question

find the domain of f(x)=1/1-2 cos x​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{f(x)=\dfrac{1}{1-2cos(x)}}$

The given function will be defined, iff $\sf{1-2cos(x)\ne0}$

So,

$\sf{cos(x)\ne\dfrac{1}{2}}$

$\sf{\implies\,cos(x)\ne\,cos\bigg(\dfrac{\pi}{3}\bigg)}$

$\sf{\implies\,x\ne\,2n\pi\pm\dfrac{\pi}{3}\,\,\,\,\,\,\,\,,\forall\,n\in\mathbb{Z}}$

$\rm{\bold{\large{Hence,\,\,domain\,\, of\,\,the\,\,function\,\,is}}}$

$\tt{\large{\bold{\pink{\mathbb{R}-\bigg\{2n\pi\pm\dfrac{\pi}{3}\bigg\}\,\,\,\,\,\,\,\,\,\,\,\,\, \forall\,n\in\mathbb{Z}}}}$