Is (1+sec^2(θ))/(sec^2(θ))=1+cos^2(θ) ?

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 + sec ^{2} ( θ )}{sec ^{2} ( θ )}

Express with sin, cos

= 1 + cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (2 a + a) = - 3 cos (a) + 4 cos^{3} (a)

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

sin (x) + cos (x) = 1

8 cos^{2} (x) - 8 sin^{2} (x) = 8 - 16 sin^{2} (x)

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

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