If $\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} = 3,$ then $\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} = $
$3$
$2$
$1$
$0$
The equation ${(a + b)^2} = 4ab\,{\sin ^2}\theta $ is possible only when
If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to
If $a\,{\cos ^3}\alpha + 3a\,\cos \alpha \,{\sin ^2}\alpha = m$ and $a\,{\sin ^3}\alpha + 3a\,{\cos ^2}\alpha \sin \alpha = n,$ then ${(m + n)^{2/3}} + {(m - n)^{2/3}}$ is equal to
The value of $\frac{{\cot 54^\circ }}{{\tan 36^\circ }} + \frac{{\tan 20^\circ }}{{\cot 70^\circ }}$ is
Find the values of other five trigonometric functions if $\sin x=\frac{3}{5}, x$ lies in second quadrant.