Is (cos^2(x))/(sin^2(x))=cot^2(x) ?

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

prove (cos^2(x))/(sin^2(x))=cot^2(x)

prove

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

True

Solution steps

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

Manipulating right side

cot^{2} (x)

Express with sin, cos

cot^{2} (x)

Use the basic trigonometric identity:

cot (x) = \frac{cos ( x )}{sin ( x )}

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

Simplify

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

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

p ro v e cot (9 0^{\circ}) = \frac{1}{tan ( 9 0 ^{\circ} )}

p ro v e \frac{- 3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

p ro v e 8 sin^{4} (θ) = cos (4 θ) + 4 cos (2 θ) - 3

p ro v e sec^{2} (a) csc^{2} (a) = sec^{2} (a) + csc^{2} (a)

p ro v e cot (x) - tan (x) = 2 tan (2 x)

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