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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating right side

cot^{2} (θ) - cos^{2} (θ)

Express with sin, cos

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

Factor

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

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

Rewrite using trig identities

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

Rewrite using trig identities

cos^{2} (θ) cot^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (θ) (1 - cos^{2} (θ)) = - cos (\frac{π}{2})

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

csc^{2} (x) tan^{2} (x) = \frac{1}{cos ^{2} ( x )}

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

cos (θ) = 2 cos^{2} (\frac{θ}{2}) - 1

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