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

The Correct Option is A

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..)