Is (1-cot(x))^2=csc^2(x)-2cot(x) ?

The answer to whether (1-cot(x))^2=csc^2(x)-2cot(x) is True

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prove (1-cot(x))^2=csc^2(x)-2cot(x)

prove

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

True

Solution steps

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

Manipulating left side

(1 - cot (x))^{2}

Expand

(1 - cot (x))^{2} : 1 - 2 cot (x) + cot^{2} (x)

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

Manipulating right side

csc^{2} (x) - 2 cot (x)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{cot ( x ) ( 1 - cos ( 2 x ) )} = csc (2 x)

tan^{4} (x) = tan^{2} (x) sec^{2} (x) - tan^{2} (x)

(tan (θ) + cot (θ)) cos (θ) = csc (θ)

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

\frac{sec ( x ) + csc ( x )}{1 + tan ( x )} = csc (x)

Is (1-cot(x))^2=csc^2(x)-2cot(x) ?
The answer to whether (1-cot(x))^2=csc^2(x)-2cot(x) is True