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

The answer to whether (cos^2(x))/(sin^2(x))+1=csc^2(x) is True

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prove (cos^2(x))/(sin^2(x))+1=csc^2(x)

prove

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

True

Solution steps

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

Manipulating right side

csc^{2} (x)

Rewrite using trig identities

= 1 + cot^{2} (x)

Express with sin, cos

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

Expand

\frac{cos ^{2} ( x ) + sin ^{2} ( x )}{sin ^{2} ( x )} : \frac{cos ^{2} ( x )}{sin ^{2} ( x )} + 1

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{csc ( x )} + 1 = \frac{1}{sin ( x )} + 1

cot (x) - cot (x) cos^{2} (x) = sin (x) cos (x)

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

\frac{1}{sec ( θ )} = arcsec (θ)

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

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