Is (tan(θ)+cot(θ))/(tan(θ))=csc^2(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ( θ ) + cot ( θ )}{tan ( 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

sin (6 0^{\circ}) = 2 sin (3 0^{\circ}) cos (3 0^{\circ})

\frac{cos ( θ )}{1 + sin ( θ )} + tan (θ) = sec (θ)

cos (x) \cdot tan (x) = sin (x)

\frac{sin ( 2 θ )}{sin ( θ )} - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

\frac{sec ( x )}{csc ( x )} + \frac{sin ( x )}{cos ( x )} = 2 tan (x)

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