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What is the domain of \(f(x)=\frac{1}{1+\sin x}\)?फलन \(f(x)=\frac{1}{1+\sin x}\) का प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \( \mathbb{R}\setminus\left{\frac{3\pi}{2}+2n\pi:n\in\mathbb{Z}\right} \)\( \mathbb{R}\setminus\left{\frac{3\pi}{2}+2n\pi:n\in\mathbb{Z}\right} \)
The denominator must not be zero, so (1+\sin x\ne 0). When \(\sin x=-1\), \(x=\frac{3\pi}{2}+2n\pi\) is excluded.हर शून्य नहीं होना चाहिए, इसलिए (1+\sin x\ne 0)। \(\sin x=-1\) पर \(x=\frac{3\pi}{2}+2n\pi\) हटेगा।
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