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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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 (x) csc (x) - sin^{2} (x) = cos^{2} (x)

tan (2 π + θ) = tan (θ)

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

cos (a) + sin (a) tan (a) = sec (a)

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

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