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On all real numbers, (aRb) if and only if (\cos^2 a=\cos^2 b). Which of the following must be in the equivalence class of (\frac{\pi}{3})?सभी वास्तविक संख्याओं पर (aRb) तब और केवल तब जब (\cos^2 a=\cos^2 b)। (\frac{\pi}{3}) के तुल्यता वर्ग में निम्न में से कौन-सी संख्या अवश्य होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{2\pi}{3})(\frac{2\pi}{3})
Step 1: (\cos\frac{\pi}{3}=\frac{1}{2}), so the squared value is (\frac{1}{4}). Step 2: (\cos\frac{2\pi}{3}=-\frac{1}{2}), whose square is also (\frac{1}{4}). Step 3: After squaring, positive and negative values may become equal.चरण 1: (\cos\frac{\pi}{3}=\frac{1}{2}), इसलिए वर्ग मान (\frac{1}{4}) है। चरण 2: (\cos\frac{2\pi}{3}=-\frac{1}{2}), इसका वर्ग भी (\frac{1}{4}) है। चरण 3: वर्ग लेने पर धनात्मक और ऋणात्मक मान समान हो सकते हैं।
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