Is sec^2(θ)-sin^2(θ)sec^2(θ)=1 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove sec^2(θ)-sin^2(θ)sec^2(θ)=1

prove

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

True

Solution steps

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

Manipulating left side

sec^{2} (θ) - sin^{2} (θ) sec^{2} (θ)

Express with sin, cos

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

Rewrite using trig identities

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

8 sin (x) cos (x) = 4 sin (2 x)

tan (x) cos (x) - \frac{1}{csc ( x )} = 0

sin^{7} (x) = (1 - cos^{2} (x))^{3} sin (x)

\frac{sec ( θ )}{csc ( θ )} = tan (θ)

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