How to prove [tan⁡(𝑥/2)]+[cot⁡(𝑥/2)] = 2csc⁡𝑥?

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Trigonometric Identities Part 1. Start solving the left-hand side members of the given equation, [tan(x/2)]+[cot(x/2)], until the right-hand side member of the given equation, 2cscx, is obtained. The left-hand side members of the given equation are now [sinx/(1+cosx)]+[(1+cosx)/sinx] after replacing tan(x/2) by sinx/(1+cosx) and cot(x/2) by 1+cosx)/sinx, these are the tangent and cotangent functions half-angle formulas respectively. Evaluate and simplify the two fractional terms.

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