Is cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x) ?

The answer to whether cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x) is True

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prove cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x)

prove

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x) = csc^{2} (2 x)

True

Solution steps

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x) = csc^{2} (2 x)

Manipulating left side

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x)

Rewrite using trig identities

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= cot^{2} (2 x) + 1

= cot^{2} (2 x) + 1

Manipulating right side

csc^{2} (2 x)

Rewrite using trig identities

csc^{2} (2 x)

Use the Pythagorean identity:

csc^{2} (x) = 1 + cot^{2} (x)

= 1 + cot^{2} (2 x)

= 1 + cot^{2} (2 x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) - 4 cos^{2} (x) = 1 - 5 cos^{2} (x)

25 sec^{2} (5 x) = 25 + (5 tan (5 x))^{2}

tan (x) = csc (2 x) - cot (2 x)

sin^{2} (- x) + cos^{2} (- x) = 1

\frac{sec ( x ) - cos ( x )}{tan ( x )} = sin (x)

Is cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x) ?
The answer to whether cot^2(2x)+cos^2(2x)+sin^2(2x)=csc^2(2x) is True