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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

= 1 + cot^{2} (x)

Rewrite using trig identities

= csc^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) (2) = sin (x) (\frac{1}{2})

cos (θ) = \frac{1}{3}

sec (θ) - \frac{tan ( θ )}{csc ( θ )} = cos (θ)

sec^{2} (x) = (1 + tan^{2} (x))

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

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