prove that (cosecA-cotA)^2=1-cosA/1+cosA​

Question

prove that (cosecA-cotA)^2=1-cosA/1+cosA​

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Adalynn 1 month 2021-08-12T18:24:37+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-12T18:25:39+00:00

    Step-by-step explanation:

    ( {cosecA - cotA})^{2}  \\  \\  = ( { \frac{1 - cosA}{sinA} })^{2}  \\  \\  =  \frac{( {1 - cosA})^{2} }{ {sin}^{2} A}  \\  \\  =  \frac{( {1 - cosA})^{2} }{1 -  {cos}^{2}A }  \\  \\  =  \frac{1  - cosA}{1 + cosA}

    0
    2021-08-12T18:26:19+00:00

    Answer:

    Given:

    The equation is,

    1cosA/1+cosA=(CosecA-cotA)²

    Solution:

    Take LHS,

    1cosA/1+cosA

    on rationalizing,

    1cosA/1+cosA×1cosA/1cosA

    =(1cosA)²/1cos²A

    =1+cos²A2cosA/sin²A

    =1/sin²A+cos²A/sin²A2cosA/sinA

    =cosec²A+cot²A-2cosecA.cotA

    =(CosecA-cotA)²

    LHS=RHS

    Step-by-step explanation:

    Hope it helps you.....

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