જો $\alpha + \beta + \gamma = 2\pi ,$ તો
$\tan \frac{\alpha }{2} + \tan \frac{\beta }{2} + \tan \frac{\gamma }{2} = \tan \frac{\alpha }{2}\tan \frac{\beta }{2}\tan \frac{\gamma }{2}$
$\tan \frac{\alpha }{2}\tan \frac{\beta }{2} + \tan \frac{\beta }{2}\tan \frac{\gamma }{2} + \tan \frac{\gamma }{2}\tan \frac{\alpha }{2} = 1$
$\tan \frac{\alpha }{2} + \tan \frac{\beta }{2} + \tan \frac{\gamma }{2} = - \tan \frac{\alpha }{2}\tan \frac{\beta }{2}\tan \frac{\gamma }{2}$
એકપણ નહિ.
જો a $cos^3 \alpha + 3a \,cos\, \alpha \, sin^2\, \alpha = m$અને $asin^3\, \alpha + 3a \, cos^2\, \alpha \,sin\, \alpha = n$ હોય તો $(m + n)^{2/3} + (m - n)^{2/3}$ =
${\sin ^4}\frac{\pi }{8} + {\sin ^4}\frac{{3\pi }}{8} + {\sin ^4}\frac{{5\pi }}{8} + {\sin ^4}\frac{{7\pi }}{8} = $
$1 + \cos 2x + \cos 4x + \cos 6x = $
સાબિત કરો કે : $\cos 4 x=1-8 \sin ^{2} x \cos ^{2} x$
If $k = \sin \frac{\pi }{{18}}\,.\,\sin \frac{{5\pi }}{{18}}\,.\,\sin \frac{{7\pi }}{{18}},$ then the numerical value of $k$ is