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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (θ) (cot (θ) + tan (θ)) = sec^{2} (θ)

sec^{2} (- θ) - 1 = tan^{2} (θ)

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

sin (- θ) sec (- θ) cot (- θ) = 1

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