Is (1+tan^2(θ))/(tan^2(θ))=csc^2(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ^{2} ( θ )}

Rewrite using trig identities

csc^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

cot (x) - 1 = csc (x) (cos (x) - sin (x))

sec (A) csc (A) = 1

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

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