Two projectiles are fired from ground with same initial speeds from same point at angles \(\left(45^{\circ}+\alpha\right)\) and \(\left(45^{\circ}-\alpha\right)\) with horizontal direction. The ratio of their times of flights is

\(\theta_1=45+\alpha ; \theta_2=45-\alpha\)
Time of flight, \(\mathrm{T}=\frac{2 \mathrm{v} \sin \theta}{\mathrm{g}}\)
\(\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\sin (45+\alpha)}{\sin (45-\alpha)}\)
\(\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\frac{1}{\sqrt{2}} \cos \alpha+\frac{1}{\sqrt{2}} \sin \alpha}{\frac{1}{\sqrt{2}} \cos \alpha-\frac{1}{\sqrt{2}} \sin \alpha}\)
\(\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\cos \alpha+\sin \alpha}{\cos \alpha-\sin \alpha}=\frac{1+\tan \alpha}{1-\tan \alpha}\)