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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{cos ^{4} ( x ) + cos ^{2} ( x ) sin ^{2} ( x )}{sin ^{2} ( x )}

Factor

\frac{cos ^{4} ( x ) + cos ^{2} ( x ) sin ^{2} ( x )}{sin ^{2} ( x )} : \frac{cos ^{2} ( x ) ( cos ^{2} ( x ) + sin ^{2} ( x ) )}{sin ^{2} ( x )}

= \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 - cos ^{4} ( x )}{sin ^{2} ( x )} = 1 + cos^{2} (x)

2 cot^{2} (A) sin^{2} (A) = 1 + cos (2 A)

sin (x) + cos (x) = cos (x) (1 + tan (x))

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

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

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