Answer
See the explanation below.
Work Step by Step
${{\cot }^{2}}2x+{{\cos }^{2}}2x+{{\sin }^{2}}2x$
Applying the Pythagorean identity of trigonometry ${{\sin }^{2}}x+{{\cos }^{2}}x=1$ , the above expression can be further simplified as:
${{\cot }^{2}}2x+{{\cos }^{2}}2x+{{\sin }^{2}}2x={{\cot }^{2}}2x+1$
By using the Pythagorean identity of trigonometry $cs{{c}^{2}}x=1+{{\cot }^{2}}x$ , the above expression can be further simplified as:
${{\cot }^{2}}2x+1=cs{{c}^{2}}2x$
Thus, the left side of the expression is equal to the right side, which is
${{\cot }^{2}}2x+{{\cos }^{2}}2x+{{\sin }^{2}}2x={{\csc }^{2}}2x$.
