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Which of the following trigonometric functions is an even function, has least positive period \(\pi\), and has range \([-1,1]\)?निम्नलिखित में से कौन-सा त्रिकोणमितीय फलन सम फलन है, जिसका न्यूनतम धनात्मक आवर्त
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Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\cos 2x\)\(\cos 2x\)
Since \(\cos(-2x)=\cos 2x\), \(\cos 2x\) is even. Replacing \(x\) by \(x+\pi\) leaves it unchanged, and its range is \([-1,1]\). Although \(\sec 2x\) is even, its range excludes values between \(-1\) and \(1\). Exam tip: test \(f(-x)\) for parity.\(\cos(-2x)=\cos 2x\), इसलिए \(\cos 2x\) सम फलन है। \(2x\) होने से इसका आवर्त \(\pi\) है और मान \([-1,1]\) में रहते हैं। \(\sec 2x\) सम है, पर उसका परास यह नहीं है। परीक्षा में समता के लिए \(f(-x)\) जाँचें।
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