Question

If $x$ is a real number such that $tanx+cotx=2$,then $x=$?

• A. $(n+\dfrac{1}{4})π,n∈Z$
• B. $(n+1)π,n∈Z$
• C. $(n+\dfrac{1}{2})π,n∈Z$
• D. $nπ,n∈Z$
• E. $\dfrac{2}{3}nπ,n∈Z$

Answer 1

Answer: (A)

$(n+\dfrac{1}{4})π,n∈Z$

Answer 2

_Give that _

Here , x is the real number

$tanx+cotx=2$

⇒tanx$$+\dfrac{1}{tanx}=2

⇒$\dfrac{(tanx)^{2}+1}{tan(x)}=2$

⇒$(tanx)^{2}-2tanx+1=0$

⇒$(tanx-1)^{2}=0$

⇒$tanx=±1$

⇒$x=\tan^{-1} (1)$

$x=\dfrac{\pi}{4}\\\\\text or \\\\\text = 3\dfrac{3\pi}{4}$

Hence ,the correct option is $(n+\dfrac{1}{4})π,n∈Z$ (Ans..)