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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1 + cos ( θ )}{tan ( θ ) + sin ( θ )} = cot (θ)

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

(tan (x) sec (- x)) cos (x) = sin (x) - 1

(1 - cos (x)) \cdot (1 - cos (x)) = (1 - cos (x))^{2}

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