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What is the range of \(f(x)=\sin x+\cos x\)?फलन \(f(x)=\sin x+\cos x\) का परिसर क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( [-\sqrt{2},\sqrt{2}] \)\( [-\sqrt{2},\sqrt{2}] \)
We have \(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\). Hence the range is \( [-\sqrt{2},\sqrt{2}] \).\(\sin x+\cos x=\sqrt{2}\sin\left(x+\frac{\pi}{4}\right)\) होता है। इसलिए परिसर \( [-\sqrt{2},\sqrt{2}] \) है।
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