Question

Let ƒ(x) = $2\pi\pi$. Then the set of values of x for which f(x) = 0, is –

• A. |2x| >$|\sin 2x|$
• B. |(2x)| <$\frac{\pi}{4}$
• C. |2x| ≥$\frac{\pi}{2}$
• D. |2x| ≤$\pi$

Answer 1

Answer: (A)

|2x| >$|\sin 2x|$

Answer 2

ƒ(x) = 0 if and only if, $\left( \frac { 3 } { \pi } \tan ^ { - 1 } 2 \mathrm { x } \right) ^ { 2 } > 1$

⇒ tan^–1 2x > $\frac { \pi } { 3 }$ or tan^–1 2x < – $\frac { \pi } { 3 }$

⇒ 2x >$\sqrt { 3 }$ or 2x < –$\sqrt { 3 }$

⇒ |2x| >$\sqrt { 3 }$

Hence (1) is the correct answer.