Question

Please explain how you prove this!! tan^2(v)(csc^2(v)-1)=1

Answer 1

If you remember the identity\[\sin^{2}v + \cos^{2}v = 1\]
You can divide the whole equation by sin^2(v) to give you\[1 + \cot^{2}v = \csc^{2}v\]
So replace csc^2v in your equation:\[\tan^{2}v [(1+\cot^{2}v) - 1] = 1\]The -1 and +1 cancel, and you if write the remaining tan^2v and cot^2v in terms of sin/cos:\[\frac{\sin^{2}v}{\cos^{2}v}\times \frac{\cos^{2}v}{\sin^{2}v} = 1\]The sins and cosines cancel, giving you \[1 = 1\]