Verify the identity. $( \tan x + \cot x ) ^ { 2 } = \sec ^ { 2 } x + \csc ^ { 2 } x$

Name: Verify the identity. $( \tan x + \cot x ) ^ { 2 } = \sec ^ { 2 } x + \csc ^ { 2 } x$
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\frac { \sin t - \csc t } { \csc t } = \frac { \sin t - \frac { 1 } { \sin t } } { \frac { 1 } { \sin t } } = \sin ^ { 2 } t - 1 = - \left( 1 - \sin ^ { 2 } t \right) = - \cos ^ { 2 } t

Verify the Identity (tan⁡x+cot⁡x)2=sec⁡2x+csc⁡2x( \tan x + \cot x ) ^ { 2 } = \sec ^ { 2 } x + \csc ^ { 2 } x(tanx+cotx)2=sec2x+csc2x