( 1+tanA)/2sinA + (1+cotA)/2cosA=cosecA + secA ​

Question

( 1+tanA)/2sinA + (1+cotA)/2cosA=cosecA + secA ​

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Ariana 4 weeks 2021-08-14T03:44:04+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-14T03:45:24+00:00

    (

    2sinA

    1+tanA

    )+(

    2cosA

    1+cotA

    )

    \displaystyle \sf{ = \bigg( \frac{1}{2 \sin A} + \frac{ \tan A}{2 \sin A} \bigg) + \bigg( \frac{1}{2 \cos A} + \frac{ \cot A}{2 \cos A} \bigg) }=(

    2sinA

    1

    +

    2sinA

    tanA

    )+(

    2cosA

    1

    +

    2cosA

    cotA

    )

    \displaystyle \sf{ = \frac{1}{2} \bigg( \csc A + \sec A \bigg) + \frac{1}{2} \bigg( \csc A + \sec A \bigg)}=

    2

    1

    (cscA+secA)+

    2

    1

    (cscA+secA)

    \displaystyle \sf{ = \bigg( \csc A + \sec A \bigg)}=(cscA+secA)

    Hence proved

    0
    2021-08-14T03:45:24+00:00

    SOLUTION

    TO PROVE

     \displaystyle \sf{ \bigg(  \frac{1 +  \tan A}{2 \sin A} \bigg) +  \bigg(  \frac{1 +  \cot A}{2 \cos A} \bigg) =  \csc  A +  \sec  A}

    PROOF

     \displaystyle \sf{ \bigg(  \frac{1 +  \tan A}{2 \sin A} \bigg) +  \bigg(  \frac{1 +  \cot A}{2 \cos A} \bigg)}

     \displaystyle \sf{  = \bigg(   \frac{1}{2 \sin A} +  \frac{ \tan A}{2 \sin A} \bigg) +  \bigg( \frac{1}{2 \cos A}   +  \frac{  \cot A}{2 \cos A} \bigg) }

     \displaystyle \sf{  =  \frac{1}{2} \bigg(  \csc  A +  \sec  A \bigg) +   \frac{1}{2} \bigg(  \csc  A +  \sec  A \bigg)}

     \displaystyle \sf{  =  \bigg(  \csc  A +  \sec  A \bigg)}

    Hence proved

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