cosecant se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
26 questions tagged with cosecant.
Where is \(\cosec x\) not defined?
B. \(x=n\pi\)
\(\cosec x=\frac{1}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। अतः \(x=n\pi\)। / Since \(\cosec x=\frac{1}{\sin x}\), it is undefined when \(\sin x=0\). Thus \(x=n\pi\).
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If \(\cosec \theta=\frac{5}{2}\) and \(\theta\) is in the first quadrant, what is \(\sin \theta\)?
C. \(\frac{2}{5}\)
\(\cosec \theta=\frac{1}{\sin \theta}\), इसलिए \(\sin \theta=\frac{2}{5}\) है। परीक्षा में cosecant और sine reciprocal हैं। / \( \cosec \theta=\frac{1}{\sin \theta}\), so \( \sin \theta=\frac{2}{5}\). In exams remember cosecant and sine are reciprocals.
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What is \(\frac{1}{\cosec x-\cot x}\) equal to?
C. \(\cosec x+\cot x\)
क्योंकि (\(\cosec x-\cot x\)\(\cosec x+\cot x\)=1)। इसलिए आवश्यक व्युत्क्रम \(\cosec x+\cot x\) है। / Since (\(\cosec x-\cot x\)\(\cosec x+\cot x\)=1). Hence the required reciprocal is \(\cosec x+\cot x\).
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What is the simplified value of \(\frac{1}{1+\cos x}+\frac{1}{1-\cos x}\)?
C. \(2\cosec^2 x\)
हरों को मिलाने पर \(\frac{2}{1-\cos^2 x}\) मिलता है। यह \(\frac{2}{\sin^2 x}=2\cosec^2 x\) है। / Combining denominators gives \(\frac{2}{1-\cos^2 x}\). This is \(\frac{2}{\sin^2 x}=2\cosec^2 x\).
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If \(\cosec x+\cot x=4\), what is the value of \(\cot x\)?
B. \(\frac{15}{8}\)
\(\cosec x-\cot x=\frac{1}{4}\) होगा। घटाने पर \(2\cot x=4-\frac{1}{4}\), इसलिए \(\cot x=\frac{15}{8}\)। / \(\cosec x-\cot x=\frac{1}{4}\). Subtracting gives \(2\cot x=4-\frac{1}{4}\), so \(\cot x=\frac{15}{8}\).
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What is the simplified value of \(\frac{\cosec x}{\cot x}\)?
B. \(\sec x\)
\(\cosec x=\frac{1}{\sin x}\) और \(\cot x=\frac{\cos x}{\sin x}\) रखें। अनुपात \(\frac{1}{\cos x}=\sec x\) होगा। / Put \(\cosec x=\frac{1}{\sin x}\) and \(\cot x=\frac{\cos x}{\sin x}\). The ratio becomes \(\frac{1}{\cos x}=\sec x\).
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How can \(\sec^2 x+\cosec^2 x\) be written in terms of \(\tan x\) and \(\cot x\)?
B. \(2+\tan^2 x+\cot^2 x\)
\(\sec^2 x=1+\tan^2 x\) और \(\cosec^2 x=1+\cot^2 x\) लगाएँ। योग \(2+\tan^2 x+\cot^2 x\) होगा। / Use \(\sec^2 x=1+\tan^2 x\) and \(\cosec^2 x=1+\cot^2 x\). The sum becomes \(2+\tan^2 x+\cot^2 x\).
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If \(\cosec x+\cot x=6\), what is the value of \(\cosec x-\cot x\)?
A. \(\frac{1}{6}\)
(\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1) होता है। इसलिए आवश्यक मान \(\frac{1}{6}\) है। / The identity is (\(\cosec x+\cot x\)\(\cosec x-\cot x\)=1). Therefore, the required value is \(\frac{1}{6}\).
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What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?
C. (1)
\(\cosec^2 x-1=\cot^2 x\) होता है। इसलिए अनुपात (1) है। / \(\cosec^2 x-1=\cot^2 x\). Hence the ratio is (1).
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If (x) is in the second quadrant and \(\cot x=-\frac{3}{4}\), what is the value of \(\cosec x\)?
A. \(\frac{5}{4}\)
\(\cosec^2 x=1+\cot^2 x\) से \(|\cosec x|=\frac{5}{4}\) मिलता है। दूसरे चतुर्थांश में \(\cosec x\) धनात्मक होता है। / From \(\cosec^2 x=1+\cot^2 x\), \(|\cosec x|=\frac{5}{4}\). In the second quadrant, \(\cosec x\) is positive.
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What is (\cosec\(\frac{\pi}{2}-x\)) equal to?
A. \(\sec x\)
(\sin\(\frac{\pi}{2}-x\)=\cos x), इसलिए (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x)। व्युत्क्रम और पूरक पहचान साथ लगाएँ। / (\sin\(\frac{\pi}{2}-x\)=\cos x), so (\cosec\(\frac{\pi}{2}-x\)=\frac{1}{\cos x}=\sec x). Use reciprocal and cofunction identities together.
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What is (\sec\(\frac{\pi}{2}-x\)) equal to?
C. \(\cosec x\)
(\cos\(\frac{\pi}{2}-x\)=\sin x), इसलिए (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x)। पूरक कोण में सहफलन बनता है। / (\cos\(\frac{\pi}{2}-x\)=\sin x), so (\sec\(\frac{\pi}{2}-x\)=\frac{1}{\sin x}=\cosec x). Complementary angles give cofunctions.
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If \(\cosec x=4\), what is the value of \(\sin x\)?
D. \(\frac{1}{4}\)
\(\cosec x=\frac{1}{\sin x}\) होता है। इसलिए \(\sin x=\frac{1}{4}\); हर व्युत्क्रम फलन को जोड़ी में याद करें। / \(\cosec x=\frac{1}{\sin x}\). Hence \(\sin x=\frac{1}{4}\); learn each reciprocal function as a pair.
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If \(\cot x=\frac{8}{15}\) and (x) is in the first quadrant, what is the value of \(\cosec x\)?
B. \(\frac{17}{15}\)
\(\cosec^2 x=1+\cot^2 x\) से \(\cosec x=\frac{17}{15}\) मिलता है। प्रथम चतुर्थांश में धनात्मक मान लें। / From \(\cosec^2 x=1+\cot^2 x\), \(\cosec x=\frac{17}{15}\). Take the positive value in the first quadrant.
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Where is \(\cosec x\) undefined?
B. \(\sin x=0\)
\(\cosec x=\frac{1}{\sin x}\) है, इसलिए \(\sin x=0\) पर यह अपरिभाषित होता है। व्युत्क्रम में नीचे वाला फलन शून्य नहीं होना चाहिए। / \(\cosec x=\frac{1}{\sin x}\), so it is undefined when \(\sin x=0\). In a reciprocal, the denominator function must not be zero.
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What is the range of \(\cosec x\)?
A. (\(-\infty,-1]\cup[1,\infty\))
\(\cosec x=\frac{1}{\sin x}\) है। इसलिए इसका परिसर (\(-\infty,-1]\cup[1,\infty\)) होता है। / \(\cosec x=\frac{1}{\sin x}\). Therefore, its range is (\(-\infty,-1]\cup[1,\infty\)).
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What is the period of the function \(\cosec x\)?
C. \(2\pi\)
\(\cosec x\) \(\sin x\) का व्युत्क्रम है और इसका काल \(2\pi\) है। व्युत्क्रम संबंध से काल पहचानें। / \(\cosec x\) is the reciprocal of \(\sin x\) and its period is \(2\pi\). Use reciprocal relation to identify the period.
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What is the value of \(\cosec^2 x-\cot^2 x\)?
B. (1)
क्योंकि \(\cosec^2 x=1+\cot^2 x\), अंतर (1) होगा। यह पहचान \(\sin^2 x+\cos^2 x=1\) से जुड़ी है। / Since \(\cosec^2 x=1+\cot^2 x\), the difference is (1). This identity is linked to \(\sin^2 x+\cos^2 x=1\).
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The function \(\cosec x\) is the reciprocal of which function?
B. \(\sin x\)
\(\cosec x=\frac{1}{\sin x}\) होता है। ध्यान रखें कि \(\cosec x\) का संबंध \(\sin x\) से है। / \(\cosec x=\frac{1}{\sin x}\). Remember that \(\cosec x\) is related to \(\sin x\).
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What is (\cosec\(2\pi-\theta\)) equal to?
A. -\(\cosec \theta\)
\(\cosec \theta\) \(\sin \theta\) का व्युत्क्रम है और चौथे चतुर्थांश में ऋणात्मक होता है। इसलिए मान \(-\cosec \theta\) है। / \(\cosec \theta\) is the reciprocal of \(\sin \theta\) and is negative in the fourth quadrant. Therefore the value is \(-\cosec \theta\).
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What is (\cosec\(\theta+2\pi\)) equal to?
C. \(\cosec \theta\)
\(\cosec \theta\) का काल \(2\pi\) है क्योंकि यह \(\sin \theta\) का व्युत्क्रम है। काल से उत्तर तुरंत मिलता है। / The period of \(\cosec \theta\) is \(2\pi\) because it is the reciprocal of \(\sin \theta\). The period gives the answer directly.
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What is (\cosec\left\(\frac{\pi}{2}+\theta\right\)) equal to?
B. \(\sec \theta\)
\(\cosec \theta\) का सह-फलन \(\sec \theta\) है और दूसरे चतुर्थांश में चिह्न धनात्मक रहता है। सह-फलन जोड़ों को याद रखें। / The cofunction of \(\cosec \theta\) is \(\sec \theta\), and the sign remains positive in the second quadrant. Remember cofunction pairs.
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When is \(\cosec \theta\) undefined?
C. जब \(\sin \theta=0\)when \(\sin \theta=0\)
\(\cosec \theta=\frac{1}{\sin \theta}\) है इसलिए \(\sin \theta=0\) पर यह अपरिभाषित होता है। हर शून्य होने पर फलन नहीं बनता। / \(\cosec \theta=\frac{1}{\sin \theta}\), so it is undefined when \(\sin \theta=0\). A function is not defined when the denominator is zero.
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What is the range of \(\cosec \theta\)?
D. (\(-\infty,-1]\cup[1,\infty\))
\(\cosec \theta=\frac{1}{\sin \theta}\) होता है। इसका परिसर (\(-\infty,-1]\cup[1,\infty\)) है। / \(\cosec \theta=\frac{1}{\sin \theta}\). Its range is (\(-\infty,-1]\cup[1,\infty\)).
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What is (\cosec\(-\theta\)) equal to?
B. \(-\cosec \theta\)
\(\cosec \theta\) विषम फलन है इसलिए (\cosec\(-\theta\)=-\cosec \theta)। यह \(\sin \theta\) के व्युत्क्रम जैसा व्यवहार करता है। / \(\cosec \theta\) is an odd function, so (\cosec\(-\theta\)=-\cosec \theta). It behaves like the reciprocal of \(\sin \theta\).
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Which trigonometric function is the reciprocal of \(\sin \theta\)?
B. \(\cosec \theta\)
\(\cosec \theta=\frac{1}{\sin \theta}\) होता है। व्युत्क्रम संबंधों को जोड़ों में याद करें। / \(\cosec \theta=\frac{1}{\sin \theta}\). Remember reciprocal relations in pairs.
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