Verify the identity secx-secx sin^2x=cosx

Question

Atticus

Mathematics

27 November, 19:38

Verify the identity secx-secx sin^2x=cosx

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Answers (1)

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Anton Wilkerson · Answer 1

Hello:

* secx = 1/cosx

cos²x+sin²x = 1

**sin²x = 1-cos²x

by (*):

secx-secx sin²x = (1/cosx) - (1/cosx) sin²x

= (1/cosx) (1 - sin²x) ... factory : (1/cosx)

by (**)

secx-secx sin²x = (1/cosx) cos²x

secx-secx sin²x = cosx ... (simplify by : cosx)