If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant
First
Second
Third
Fourth
If $\left| {\,a\,{{\sin }^2}\theta + b\sin \theta \cos \theta + c\,{{\cos }^2}\theta - \frac{1}{2}(a + c)\,} \right|\, \le \frac{1}{2}k,$ then ${k^2}$ is equal to
Prove that :
$\cot ^{2} \frac{\pi}{6}+\cos ec \,\frac{5 \pi}{6}+3 \tan ^{2}\, \frac{\pi}{6}=6$
If $\sin {\theta _1} + \sin {\theta _2} + \sin {\theta _3} = 3,$ then $\cos {\theta _1} + \cos {\theta _2} + \cos {\theta _3} = $
$\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }} = $