Match the following for the trigonometric equation |x+ 1 4 |- |x- 1 4 | = cos πx, (n is…
Mathematics · JEE Advanced · NTA Exams — Trigonometry
Match the following for the trigonometric equation \(\left|x+\frac{1}{4}\right|-\left|x-\frac{1}{4}\right|\) = cos πx, (n is an integer) :
Column - I Column - II
( a) Over \(\left(-\infty,-\frac{1}{4}\right)\) (p) \(\left\{\frac{1}{3}\right\} \cup\left\{2 n \pm \frac{1}{3}, n>0\right\}\)
(B) Over \(\left[-\frac{1}{4}, \frac{1}{4}\right]\) (Q) \(\left\{-\frac{2}{3}\right\} \cup\left\{2 \mathrm{n} \pm \frac{2}{3}, \mathrm{n}<0\right\}\)
(C) Over \(\left(\frac{1}{4}, \infty\right)\) (R) No solution
Correct Matching is
Column - I Column - II
( a) Over \(\left(-\infty,-\frac{1}{4}\right)\) (p) \(\left\{\frac{1}{3}\right\} \cup\left\{2 n \pm \frac{1}{3}, n>0\right\}\)
(B) Over \(\left[-\frac{1}{4}, \frac{1}{4}\right]\) (Q) \(\left\{-\frac{2}{3}\right\} \cup\left\{2 \mathrm{n} \pm \frac{2}{3}, \mathrm{n}<0\right\}\)
(C) Over \(\left(\frac{1}{4}, \infty\right)\) (R) No solution
Correct Matching is
- A–Q; B–R; C–P
- A–R; B–Q; C–P
- A–P; B–R; C–Q
- A–P; B–Q; C–R
Answer
(A) A–Q; B–R; C–P
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