Verify identities Will give BRAINLIST do not give me trash!! cot^2(x) – csc^2(x) = -1 show steps

Question

Verify identities Will give BRAINLIST do not give me trash!!

cot^2(x) – csc^2(x) = -1

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Edana Edana 4 years 2021-08-09T19:52:40+00:00 1 Answers 15 views 0

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    2021-08-09T19:54:32+00:00

    Answer:

    See proof below

    Step-by-step explanation

    cot^2(x) – csc^2(x) = -1

    In trigonometry identity

    cot^2x = cos²x/sin²x

    Csc²x = 1/sin²x

    Substitute into the original expression

    cos²x/sin²x – 1/sin²x

    Find the LCM

    (Cos²x-1)/sin²x …. *

    Recall that sin²x+cos²x = 1

    Sin²x = 1-cos²x

    -sin²x = -1+cos²x

    -sin²x = cos²x-1 …. **

    Substitute ** into *

    (Cos²x-1)/sin²x

    -sin²x/sin²x

    = -1 (RHS)

    Therefore cot^2(x) – csc^2(x) = -1 (Proved!)

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )