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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) - \frac{1}{sin ( θ )} = cos (θ)

cos^{8} (x) = sin^{7} (x) cos^{1} (x)

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

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

cos (θ) = \frac{1}{3}

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