Question

tanx- sec^2x/tanx=-cotx verify the identity

Answer 1

Multiply through by tanx and you'll have something that should look familiar.

Answer 2

\[\tan^2(x) +1 = \sec^2(x)\] We will sue this identity.
\[-\cot(x) = \tan(x) - \sec^2(x)/\tan(x) \]
\[-\cot(x) = [\tan^2(x) -sex^2(x)]/\tan(x) \]
Use the identity above
\[-\cot(x)= [\tan^2(x) - (\tan^2(x) - 1]/\tan(x)\]
\[-\cot(x) = - 1/\tan(x)\]

1/tan(x) is cot(x) so
-cot(x) = -cot(x)

Answer 3

That 1 should be positive then become negative when distributing the negative sign.