જો x = frac{{npi }}{2} એ સમીકરણ sin, frac{x}{ | vedclass

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Question

$\left| {\frac{x}{2} - \frac{\pi }{2}} \right| \le \frac{{3\pi }}{4}$ possible $x$ are

$\begin{array}{l} - \frac{{3\pi }}{4} \le \frac{x}{2} -

Vedclass · Accepted Answer

$n = 1, 2, 4, 5$

Vedclass · Answer

$\left| {\frac{x}{2} - \frac{\pi }{2}} ight| \le \frac{{3\pi }}{4}$ possible $x$ are

$\begin{array}{l} - \frac{{3\pi }}{4} \le \frac{x}{2} - \frac{\pi }{2} \le \frac{{3\pi }}{4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - \frac{\pi }{2},0,\frac{\pi }{2},\pi ,\frac{{3\pi }}{2},2\pi ,\frac{{5\pi }}{2}\ - \frac{\pi }{4} \le \frac{x}{2} \le \frac{{5\pi }}{4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\sin \frac{x}{2} - \cos \frac{x}{2} = {(\sin \frac{x}{2} - \cos \frac{x}{2})^2}\ - \frac{\pi }{2} \le x \le \frac{{5\pi }}{4}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,factors\,\sin \frac{x}{2} - \cos \frac{x}{2} = \\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,or\,\,\,\,\,\,\,\,\sin \frac{x}{2} - \cos \frac{x}{2} = 1\end{array}$

only circled angle satisfy one of the above equation when $n = 1, 2, 4, 5$

જો $x = \frac{{n\pi }}{2}$ એ સમીકરણ $sin\, \frac{x}{2}- cos \frac{x}{2} = 1$ $- sin\, x$ & અસમતા $\left| {\frac{x}{2}\,\, - \,\,\frac{\pi }{2}} \right|\,\, \le \,\,\frac{{3\pi }}{4}$ ને સંતોષે તો

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