If $a\cos \theta + b\sin \theta = m$ and $a\sin \theta - b\cos \theta = n,$ then ${a^2} + {b^2} = $
$m + n$
${m^2} - {n^2}$
${m^2} + {n^2}$
None of these
Which of the following relations is correct
Find the values of other five trigonometric functions if $\sec x=\frac{13}{5}, x$ lies in fourth quadrant.
If $\sin \theta + {\rm{cosec}}\theta = {\rm{2}}$, then ${\sin ^2}\theta + {\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta = $
Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$
If $x{\sin ^3}\alpha + y{\cos ^3}\alpha = \sin \alpha \cos \alpha $ and $x\sin \alpha - y\cos \alpha = 0,$ then ${x^2} + {y^2} = $