show that (cotA-1+cosecA) /(CotA+1-cosecA)=cotA+cosecA​

Question

show that (cotA-1+cosecA) /(CotA+1-cosecA)=cotA+cosecA​

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Ariana 1 month 2021-08-18T23:42:28+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-18T23:43:30+00:00

    \huge\boxed{\underline{\underline{\green{\tt Solution}}}}

    Solution

    \displaystyle \: \frac{CotA – 1 + CosecA}{CotA + 1 – CosecA}

    CotA+1−CosecA

    CotA−1+CosecA

    = \displaystyle \: \frac{CotA + CosecA – 1}{CotA – CosecA + 1}=

    CotA−CosecA+1

    CotA+CosecA−1

    = \displaystyle \: \frac{CotA + CosecA – ( {Cosec}^{2}A – {Cot}^{2}A) }{CotA + 1 – CosecA}=

    CotA+1−CosecA

    CotA+CosecA−(Cosec

    2

    A−Cot

    2

    A)

    =\frac{(CotA + CosecA )-(CosecA + CotA )(CosecA – CotA ) }{CotA + 1 – CosecA}=

    CotA+1−CosecA

    (CotA+CosecA)−(CosecA+CotA)(CosecA−CotA)

    = \frac{(CotA + CosecA )(CotA + 1 – CosecA)}{(CotA + 1 – CosecA)}=

    (CotA+1−CosecA)

    (CotA+CosecA)(CotA+1−CosecA)

    = (CotA + CosecA)=(CotA+CosecA)

    0
    2021-08-18T23:43:40+00:00

    \huge\boxed{\underline{\underline{\green{\tt Solution}}}}

      \displaystyle \: \frac{CotA - 1 + CosecA}{CotA  + 1  - CosecA}

     =   \displaystyle \: \frac{CotA  + CosecA - 1}{CotA    - CosecA + 1}

     =   \displaystyle \: \frac{CotA  + CosecA - ( {Cosec}^{2}A -  {Cot}^{2}A)  }{CotA  + 1  - CosecA}

     =\frac{(CotA  + CosecA )-(CosecA  + CotA )(CosecA   -  CotA ) }{CotA  + 1  - CosecA}

     =   \frac{(CotA  + CosecA )(CotA  + 1  - CosecA)}{(CotA  + 1  - CosecA)}

     = (CotA  + CosecA)

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