Prove that

1 / cos (x) - cos (x) = sin (x) ∙ tan (x) for x ≠?2 + k, for all integers k.

Question

Brice Lamb

Mathematics

17 June, 20:12

Prove that

1 / cos (x) - cos (x) = sin (x) ∙ tan (x) for x ≠?2 + k, for all integers k.

+4

Answers (1)

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Rosales · Answer 1

Answer: From the given expression we can get the fundamental trigonometry identity

Step-by-step explanation:

1 : cos (*) - cos (*) = sin (*) * tan (*) ⇒

[1 : cos (*) ] - cos (*) = sin (*) * sin (*) / cos (*)

1 / cos (*) - cos (*) = sin² (*) / cos (*) ⇒cos (*) / cos (*) - cos² (*) = sin² (*)

1 - cos² (*) = sin² (*)

1 = cos² (*) + sin² (*) fundamental trigonometry identity

Prove that1 / cos (x) - cos (x) = sin (x) ∙ tan (x) for x ≠?2 + k, for all integers k.

Prove that

1 / cos (x) - cos (x) = sin (x) ∙ tan (x) for x ≠?2 + k, for all integers k.