If $\frac{{\cos x}}{a} = \frac{{\cos (x + \theta )}}{b} = \frac{{\cos (x + 2\theta )}}{c} = \frac{{\cos (x + 3\theta )}}{d} \, ,$ then $\left( {\frac{{a + c}}{{b + d}}} \right)$ is equal to :-
$\frac{a}{d}$
$\frac{c}{d}$
$\frac{b}{c}$
$\frac{d}{a}$
If $x = sec\, \phi - tan\, \phi$ & $y = cosec\, \phi + cot\, \phi$ then :
$\frac{{\sin {{81}^o} + \cos {{81}^o}}}{{\sin {{81}^o} - \cos {{81}^o}}}$ is equal to
If $\sin A + \cos A = \sqrt 2 ,$ then ${\cos ^2}A = $
$\tan 75^\circ - \cot 75^\circ = $
The value of $\cot {70^o} + 4\cos {70^o}$ is