Is tan(θ/2)=csc(θ)-cot(θ) ?

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

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prove tan(θ/2)=csc(θ)-cot(θ)

prove

tan (\frac{θ}{2}) = csc (θ) - cot (θ)

True

Solution steps

tan (\frac{θ}{2}) = csc (θ) - cot (θ)

Let:

u = \frac{θ}{2}

tan (u) = csc (2 u) - cot (2 u)

Prove

tan (u) = csc (2 u) - cot (2 u) :

True

Therefore

tan (\frac{θ}{2}) = csc (θ) - cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (4 x) = 1 - 8 sin^{2} (x) + 8 sin^{4} (x)

(sin (θ) - cos (θ))^{2} = 1 - sin (2 θ)

\frac{sec ( x )}{csc ( x )} = tan (x)

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

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

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