Is 1/(1+tan^2(θ))=cos^2(θ) ?

The answer to whether 1/(1+tan^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 1/(1+tan^2(θ))=cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{1 + tan ^{2} ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan (\frac{π}{4} - t) = \frac{1 - tan ( t )}{1 + tan ( t )}

- tan (x) = tan (- x)

\frac{csc ( θ ) + sin ( θ )}{tan ( θ ) + 1} = csc (θ)

Is 1/(1+tan^2(θ))=cos^2(θ) ?
The answer to whether 1/(1+tan^2(θ))=cos^2(θ) is True