Is (1-sin^2(x))/(csc^2(x)-1)=sin^2(x) ?

The answer to whether (1-sin^2(x))/(csc^2(x)-1)=sin^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-sin^2(x))/(csc^2(x)-1)=sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (2 θ) = 1 - 2 sin^{2} (θ)

sin (x) = 1 - cos (x)

\frac{cos ( θ )}{cot ( θ )} = sin (θ)

sin (θ) = \frac{tan ( θ )}{sec ( θ )}

\frac{sec ( y )}{tan ( y ) + cot ( y )} = sin (y)

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