Mathematics: Prove the identities (sec x + sin x)cot x = CSC x + cos X

Prove the identities (sec x + sin x)cot x = CSC

Ответ:

laqu33n021

19.01.2022

Step-by-step explanation:

$(sec \: x + sin \: x)cot \: x = csc \: x + cos \: x \\ \\ LHS = (sec \: x + sin \: x)cot \: x \\ = (sec \: x + sin \: x) \times \frac{cos \: x}{sin \: x} \\ \\ = sec \: x \times \frac{cos \: x}{sin \: x} + sin \: x \times \frac{cos \: x}{sin \: x} \\ \\ = \frac{1}{cos\: x } \times \frac{cos \: x}{sin \: x} + sin \: x \times \frac{cos \: x}{sin \: x} \\ \\ = \frac{1}{sin \: x} + cos \: x\\ \\ = csc \: x+ cos \: x \\ = RHS \\ \\ \therefore \: (sec \: x + sin \: x)cot \: x = csc \: x + cos \: x \\ thus \: proved$

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Ответ:

bradleycawley02

28.02.2023

Mathematics

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Prove the identities (sec x + sin x)cot x = CSC x + cos X

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