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

The answer to whether (1-cot^2(x))/(tan^2(x)-1)=cot^2(x) is True

Popular >

prove (1-cot^2(x))/(tan^2(x)-1)=cot^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 - cot ^{2} ( x )}{tan ^{2} ( x ) - 1}

Express with sin, cos

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

Rewrite using trig identities

cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) tan (x) = sec (x)

\frac{1 cot ( x )}{csc ( x )} = sin (x) cos (x)

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

cot (x) sec (x) sin (x) = 1

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

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