Is tan(x/2)=-cot(x)+csc(x) ?

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

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prove tan(x/2)=-cot(x)+csc(x)

prove

tan (\frac{x}{2}) = - cot (x) + csc (x)

True

Solution steps

tan (\frac{x}{2}) = - cot (x) + csc (x)

Let:

u = \frac{x}{2}

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

Prove

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

True

Therefore

tan (\frac{x}{2}) = - cot (x) + csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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\frac{cos ^{3} ( t )}{cot ^{2} ( t )} = sin^{2} (t) cos (t)

cos (a + b) cos (a - b) = cos^{2} (a) - cos^{2} (b)

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