Question

prove and justify (tanN + cotN)^2=sec^2N+csc^2 N

Answer 1

\[=\tan^{2}N + 2\tan N \cot N +\cot^{2} N\]
Note: tan*cot = 1
\[= \tan^{2} N +2 +\cot^{2} N\]
from pythagorean identities
tan^2 = sec^2 -1
cot^2 = csc^2 -1
\[=(\sec^{2} N -1) +2+(\csc^{2} N -1)\]
\[=\sec^{2} N + \csc^{2} N\]