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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{cot ^{2} ( x )}{1 + cot ^{2} ( x )}

Express with sin, cos

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

Rewrite using trig identities

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (6 0^{\circ}) = 2 cos^{2} (3 0^{\circ}) - 1

(sin (t) + cos (t))^{2} = 1 + sin (2 t)

sec^{2} (θ) = \frac{1}{cos ^{2} ( θ )}

csc^{2} (θ) = \frac{1}{sin ^{2} ( θ )}

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

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