Is (1+tan^2(x))(1-sin^2(x))=1 ?

The answer to whether (1+tan^2(x))(1-sin^2(x))=1 is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (1+tan^2(x))(1-sin^2(x))=1

prove

(1 + tan^{2} (x)) (1 - sin^{2} (x)) = 1

True

Solution steps

(1 + tan^{2} (x)) (1 - sin^{2} (x)) = 1

Manipulating left side

(1 + tan^{2} (x)) (1 - sin^{2} (x))

Rewrite using trig identities

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

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( θ )}{1 - sin ( θ )} = \frac{sin ( θ ) - csc ( θ )}{cos ( θ ) - cot ( θ )}

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

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

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

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

Is (1+tan^2(x))(1-sin^2(x))=1 ?
The answer to whether (1+tan^2(x))(1-sin^2(x))=1 is True