Is cos^2(θ)(sec^2(θ)-1)=sin^2(θ) ?

The answer to whether cos^2(θ)(sec^2(θ)-1)=sin^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)(sec^2(θ)-1)=sin^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (θ) (sec^{2} (θ) - 1)

Express with sin, cos

= 1 - cos^{2} (θ)

Rewrite using trig identities

= sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot^{2} (y) sec^{2} (y) = 1 + cot^{2} (y)

csc (θ) - cot (θ) \cdot cos (θ) = sin (θ)

\frac{cos ( x )}{1 - sin ( x )} = tan (x) + sec (x)

cot (x) + tan (x) = \frac{sec ^{2} ( x )}{tan ( x )}

\frac{1}{cos ( x )} = sec (x)

Is cos^2(θ)(sec^2(θ)-1)=sin^2(θ) ?
The answer to whether cos^2(θ)(sec^2(θ)-1)=sin^2(θ) is True