यदि $\cos \,(\theta - \alpha ) = a,\,\,\sin \,(\theta - \beta ) = b,\,\,$ हो, तब ${\cos ^2}(\alpha - \beta ) + 2ab\,\sin \,(\alpha - \beta )$ बराबर है
$4{a^2}{b^2}$
${a^2} - {b^2}$
${a^2} + {b^2}$
$ - {a^2}{b^2}$
निम्नलिखित को सिद्ध कीजिए
$\frac{\sin x+\sin 3 x}{\cos x+\cos 3 x}=\tan 2 x$
यदि $\frac{x}{{\cos \theta }} = \frac{y}{{\cos \left( {\theta - \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \left( {\theta + \frac{{2\pi }}{3}} \right)}},$ तो $x + y + z = $
$\frac{1}{{\tan 3A - \tan A}} - \frac{1}{{\cot 3A - \cot A}} = $
यदि $\tan \alpha = \frac{1}{7}$ तथा $\sin \beta = \frac{1}{{\sqrt {10} }}\left( {0 < \alpha ,\,\beta < \frac{\pi }{2}} \right)$, तब $2\beta $ बराबर है
$\sin {163^o}\cos {347^o} + \sin {73^o}\sin {167^o} = $