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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

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

sin (\frac{π}{6} + x) = cos (\frac{π}{3} - x)

2 cos^{2} (x) - 1 = 0

(1 + cos (2 θ)) (1 - cos (2 θ)) = sin^{2} (2 θ)

sin (x) - cos (x) = 0

sin (2 θ) + cos (2 θ) = 2 sin (θ) cos (θ) + 2 cos^{2} (θ) - 1

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