1-COS A ii) sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A sin A) cos) (cort​

Question

1-COS A
ii) sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A
sin A)
cos)
(cort​

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Luna 4 weeks 2021-08-18T09:42:19+00:00 1 Answer 0 views 0

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    2021-08-18T09:43:42+00:00

    ✒️QUESTION✒️

     \small{ \sf  \dag\sin A(1 +  \tan A )+  \cos A(1 +  \cot A ) =  \sec A   +  \cosec A }

    ✒️ANSWER✒️

    ☄️GIVEN☄️

     \small{  \sf \bull \sin A(1 +  \tan A )+  \cos A(1 +  \cot A ) =  \sec A   +  \cosec A }

    ☄️PROVE THAT☄️

     \sf{ \bull L.H.S = R.H.S}

    ☄️PROOF☄️

    L.H.S

    \sf  ➔ \sin A(1 +  \tan A )+  \cos A(1 +  \cot A )

    \sf  ➔ \sin A +  \sin A \tan A +  \cos A +  \cos A \cot A

    \sf  ➔ \sin A +  \sin A  \times  \frac{ \sin A}{\cos A}  +  \cos A +  \cos A  \times  \frac{\cos A}{\sin A}

    \sf  ➔ \sin A + \frac{{\cos}^2 A}  { \sin A} +   \cos A +  \frac{{\sin}  ^ 2A } {\cos A}

    \sf  ➔   \frac{  {\sin}^{2}A   + {\cos}^2 A}  { \sin A} +    \frac{{\cos}^2 A +    {\sin}^{2}A }{ \cos A }

    \sf  ➔   \frac{  1}  { \sin A} +    \frac{1}{ \cos A }  \:  \:  \:  \: ( { \sin}^{2} A +   { \cos}^{2} A = 1)

     \sf =  \cosec A +  \sec A

    L.H.S = R.H.S

    HENCE, PROVED.

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