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11 August, 07:11

Which of the following is not an identity?

A. cos^2 x csc x - csc x = - sin x

B. sin x (cot x + tan x) = sec x

C. cos^2 x - sin^2 x = 1 - 2sin^2 x

D. csc^2 x + sec^2 x = 1

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Answers (1)
  1. 11 August, 11:02
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    A) cos² x · 1 / sin x - 1 / sin x = - sin x

    cos² x - 1 / sin x = - sin x

    - sin² x / sin x = - sin x

    - sin x = - sin x (correct)

    B) sin x (cos x / sin x + sin x / cos x) = 1 / cos x

    sin x · (cos² x + sin²x) / sin x cos x = 1 / cos x

    sin x · 1 / sin x cos x = 1 / cos x

    1 / cos x = 1 / cos x (correct)

    C) cos² x - sin² x = 1 - 2 sin² x

    1 - sin² x - sin² x = 1 - 2 sin² x

    1 - 2 sin² x = 1 - 2 sin² x (correct)

    D) 1/sin²x + 1 / cos²x = 1

    cos²x + sin² x / sin² x cos² x = 1

    1 / cos² x sin² x = 1

    cos²x sin² x ≠ 1

    Answer: D) is not an identity.
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