general-solution se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
10 questions tagged with general-solution.
If \(\tan x=\tan y\), what is the general solution?
C. \(x=n\pi+y\)
\(\tan x\) का आवर्त \(\pi\) है, इसलिए \(x=n\pi+y\) होगा। परीक्षा में tangent के लिए \(n\pi\) जोड़ें। / The period of \(\tan x\) is \(\pi\), so \(x=n\pi+y\). In exams, add \(n\pi\) for tangent.
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If \(\cos x=\cos y\), what is the correct form of the general solution?
B. \(x=2n\pi\pm y\)
\(\cos x=\cos y\) के लिए कोण \(2n\pi\pm y\) के रूप में आते हैं। परीक्षा में cosine की सम प्रकृति याद रखें। / For \(\cos x=\cos y\), angles are of the form \(2n\pi\pm y\). In exams, remember the even nature of cosine.
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If \(\sin x=\sin y\), which relation can generally be true?
A. \(x=2n\pi+y\) या (x=(2n+1)\pi-y)\(x=2n\pi+y\) or (x=(2n+1)\pi-y)
\(\sin x=\sin y\) के लिए (x=n\pi+(-1)^n y) होता है। इसी से दिए गए दोनों रूप मिलते हैं। / For \(\sin x=\sin y\), (x=n\pi+(-1)^n y). This gives the two stated forms.
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If \(\cos \theta=-1\), what is the general solution for \(\theta\)?
B. (\theta=(2n+1)\pi)
\(\cos \theta=-1\) विषम गुणजों of \(\pi\) पर होता है। परीक्षा में \(\cos \theta=1\) और \(\cos \theta=-1\) के हल अलग पहचानें। / \( \cos \theta=-1\) occurs at odd multiples of \( \pi\). In exams distinguish the solutions of \( \cos \theta=1\) and \( \cos \theta=-1\).
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If \(\tan \theta=\tan \alpha\), what is the general solution?
B. \(\theta=n\pi+\alpha\)
\(\tan \theta\) का period \(\pi\) है इसलिए हल \(\theta=n\pi+\alpha\) होगा। परीक्षा में tangent equations में \(\pi\) period लगाएं। / The period of \( \tan \theta\) is \( \pi\), so the solution is \( \theta=n\pi+\alpha\). In exams use period \( \pi\) for tangent equations.
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If \(\cos \theta=\cos \alpha\), which is the general solution?
B. \(\theta=2n\pi\pm\alpha\)
\(\cos \theta=\cos \alpha\) के लिए दोनों दिशाओं में कोण मिलते हैं। परीक्षा में \(\pm\alpha\) लगाना न भूलें। / For \( \cos \theta=\cos \alpha\), angles occur in both directions. In exams do not forget \( \pm\alpha\).
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If \(\sin \theta=\sin \alpha\), which is the general solution?
A. (\theta=n\pi+(-1)^n\alpha)
\(\sin \theta=\sin \alpha\) का संयुक्त हल (\theta=n\pi+(-1)^n\alpha) होता है। परीक्षा में दो अलग हलों को एक सूत्र में लिखना सीखें। / The combined solution of \( \sin \theta=\sin \alpha\) is ( \theta=n\pi+(-1)^n\alpha). In exams learn to write two cases in one formula.
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What is the general solution of \(\tan \theta=0\)?
A. \(\theta=n\pi\)
\(\tan \theta=0\) तब होता है जब \(\sin \theta=0\) और \(\cos \theta\neq0\)। परीक्षा में tangent का period \(\pi\) रखें। / \( \tan \theta=0\) occurs when \( \sin \theta=0\) and \( \cos \theta\neq0\). In exams use period \( \pi\) for tangent.
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If \(\cos \theta=0\), what is the general solution for \(\theta\)?
B. (\theta=\frac{(2n+1)\pi}{2})
\(\cos \theta\) शून्य odd multiples of \(\frac{\pi}{2}\) पर होता है। परीक्षा में (\frac{(2n+1)\pi}{2}) पैटर्न याद रखें। / \( \cos \theta\) is zero at odd multiples of \( \frac{\pi}{2}\). In exams remember the pattern ( \frac{(2n+1)\pi}{2}).
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If \(\sin \theta=0\), what is the general solution for \(\theta\)?
A. \(\theta=n\pi\)
\(\sin \theta\) शून्य (0), \(\pi\), \(2\pi\) जैसे बिंदुओं पर होता है। परीक्षा में \(n\in\mathbb{Z}\) मानकर सामान्य हल लिखें। / \( \sin \theta\) is zero at points like (0), \(\pi\), and \(2\pi\). In exams write the general solution with \(n\in\mathbb{Z}\).
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