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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Factor

\frac{cos ^{2} ( x ) - cos ^{2} ( x ) sin ^{2} ( x )}{sin ^{2} ( x )} : \frac{cos ^{2} ( x ) ( 1 - sin ^{2} ( x ) )}{sin ^{2} ( x )}

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

Rewrite using trig identities

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

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (a) = cos (9 0^{\circ} + a)

cot (θ) + tan (θ) = 2 csc (2 θ)

tan^{2} (a) - sin^{2} (a) = tan^{2} (a) sin^{2} (a)

cos (x) (tan (x) - sec (- x)) = sin (x) - 1

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

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