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What type of function is (f(x)=\sin x\cos x)?फलन (f(x)=\sin x\cos x) किस प्रकार का है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Odd functionविषम फलन
Given \(f(x)=\sin x\cos x\). Therefore, \(f(-x)=\sin(-x)\cos(-x)=(-\sin x)(\cos x)=-\sin x\cos x=-f(x)\). Hence, the function is odd. For an even function, we would need \(f(-x)=f(x)\), which is not true here. Exam tip: \(\sin x\) is odd and \(\cos x\) is even; the product of an odd and an even function is odd.दिया है \(f(x)=\sin x\cos x\)। अतः \(f(-x)=\sin(-x)\cos(-x)=(-\sin x)(\cos x)=-\sin x\cos x=-f(x)\)। इसलिए यह विषम फलन है। सम फलन के लिए \(f(-x)=f(x)\) होना चाहिए, जो यहाँ सत्य नहीं है। परीक्षा टिप: \(\sin x\) विषम और \(\cos x\) सम होता है; विषम तथा सम फलनों का गुणनफल विषम होता है।
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