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

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

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prove (1+tan^2(x))/(tan^2(x))=csc^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

csc^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

(1 + tan^{2} (x)) cot^{2} (x) = csc^{2} (x)

csc (θ) sec (θ) - cot (θ) = tan (θ)

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

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

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