કોઈ પણ $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$ માટે, $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ =
કોઈ પણ $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$ માટે, $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ =
- [JEE MAIN 2019]
- A
$13 - 4\,{\cos ^2}\,\theta \, + 6\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
- B
$13 - 4\,{\cos ^6}\,\theta \,$
- C
$13 - 4\,{\cos ^2}\,\theta \, + 6\,\,{\cos ^4}\,\theta $
- D
$13 - 4\,{\cos ^4}\,\theta \, + 2\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
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$cot 5^o$ -$tan5^o$ -$2$ $tan10^o$ -$4$ $tan 20^o$ -$8$ $cot40^o$ =
જો $3\cos \theta + 4\sin \theta = 5$ અને $3\sin \theta - 4\cos \theta $ =
જો $3\cos \theta + 4\sin \theta = 5$ અને $3\sin \theta - 4\cos \theta $ =
જો $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ તો $x = $
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$\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}} = . . . .$
$\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}} = . . . .$
- [IIT 1991]
$A, B, C$ એ ત્રિકોણના ખૂણા હોય ,તો ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $
$A, B, C$ એ ત્રિકોણના ખૂણા હોય ,તો ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C - 2\cos A\,\cos B\,\cos C = $