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Prove the Identity: cos x (sec x - cos x) = sin^2 x?
Pls, help.
1 Answer
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- germanoLv 74 years ago
Hello,
cosx (secx - cosx) = sin²x
let's recall that secx = 1 /cosx:
cosx [(1 /cosx) - cosx] = sin²x
cosx [(1 - cos²x) /cosx] = sin²x
(simplifying)
1 - cos²x = sin²x
(applying the fundamental identity 1 = sin²x + cos²x)
(sin²x + cos²x) - cos²x = sin²x
sin²x + cos²x - cos²x = sin²x
sin²x = sin²x (Q.E.D.)
I hope it helps
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