If $A + B + C = \pi ,$ then $\frac{{\cos A}}{{\sin B\sin C}} + \frac{{\cos B}}{{\sin C\sin A}} + \frac{{\cos C}}{{\sin A\sin B}} = $
$0$
$1$
$2$
$3$
If $A$ lies in the third quadrant and $3\ tanA - 4 = 0$ , then find the value of $5\ sin\ 2A + 3\ sinA + 4\ cosA$
Prove that $\frac{\sin x+\sin 3 x}{\cos x+\cos 3 x}=\tan 2 x$
If $x = sec\, \phi - tan\, \phi$ & $y = cosec\, \phi + cot\, \phi$ then :
$\cos 20^\circ \cos 40^\circ \cos 80^\circ = $
If $\tan x = \frac{{2b}}{{a - c}}(a \ne c),$
$y = a\,{\cos ^2}x + 2b\,\sin x\cos x + c\,{\sin ^2}x$
and $z = a{\sin ^2}x - 2b\sin x\cos x + c{\cos ^2}x,$ then