Is 1/(1-cos^2(x))=1+cot^2(x) ?

The answer to whether 1/(1-cos^2(x))=1+cot^2(x) 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-cos^2(x))=1+cot^2(x)

prove

\frac{1}{1 - cos ^{2} ( x )} = 1 + cot^{2} (x)

True

Solution steps

\frac{1}{1 - cos ^{2} ( x )} = 1 + cot^{2} (x)

Manipulating right side

1 + cot^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

tan^{4} (k) - sec^{4} (k) = 1 - 2 sec^{2} (k)

tan^{2} (x) + 5 = sec^{2} (x) + 4

1 - tan^{4} (x) = 2 sec^{2} (x) - sec^{4} (x)

Is 1/(1-cos^2(x))=1+cot^2(x) ?
The answer to whether 1/(1-cos^2(x))=1+cot^2(x) is True