Is csch^2(x)=coth^2(x)-1 ?

The answer to whether csch^2(x)=coth^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 csch^2(x)=coth^2(x)-1

prove

csch^{2} (x) = coth^{2} (x) - 1

True

Solution steps

csch^{2} (x) = coth^{2} (x) - 1

Manipulating right side

coth^{2} (x) - 1

Rewrite using trig identities

= \frac{cosh ^{2} ( x ) - sinh ^{2} ( x )}{sinh ^{2} ( x )}

Rewrite using trig identities

= csch^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sec ( x ) + tan ( x )} = sec (x) - tan (x)

\frac{tan ( y )}{csc ( y )} = \frac{1}{cos ( y )} - \frac{1}{sec ( y )}

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

2 tan (x) sec (x) = \frac{1}{1 - sin ( x )} - \frac{1}{1 + sin ( x )}

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