જો $\frac{{\cos x}}{a} = \frac{{\cos (x + \theta )}}{b} = \frac{{\cos (x + 2\theta )}}{c} = \frac{{\cos (x + 3\theta )}}{d} \, ,$ હોય તો  $\left( {\frac{{a + c}}{{b + d}}} \right)$ = 

જો $\tan A = \frac{1}{2},$ તો $\tan 3A = $

જો $A + B + C = {180^o},$ તો $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}  = . . .$

સમીકરણ $\frac{{{{\tan }^2}20^\circ  - {{\sin }^2}20^\circ }}{{{{\tan }^2}20^\circ \,\cdot\,{{\sin }^2}20^\circ }}$ = 

જો ${\rm{cosec}}\theta = \frac{{p + q}}{{p - q}},$ તો $\cot \,\left( {\frac{\pi }{4} + \frac{\theta }{2}} \right) = $

જો $0 < x , y < \pi$ અને $\cos x +\cos y-\cos ( x + y )=\frac{3}{2}$ હોય, તો $\sin x+\cos y =$ ...... .