If (1 – sin A) (1- sin B) (1- sin C) = (1 + sin A) (1+ sin B) (1+ sin C), then prove that each side is equal to cos A cos B cos C.

Question

If (1 – sin A) (1- sin B) (1- sin C) = (1 + sin A) (1+ sin B) (1+ sin C), then prove that each side is equal to cos A cos B cos C.

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Iris 1 month 2021-08-13T01:13:04+00:00 1 Answer 0 views 0

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    2021-08-13T01:14:21+00:00

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

    Let

    k = (1 - sin A) (1- sin B) (1- sin C) = (1 + sin A) (1+ sin B) (1+ sin C)

    Now

    k \times k = (1 - sin A) (1- sin B) (1- sin C)  \times  (1 + sin A) (1+ sin B) (1+ sin C)

     \implies \:  {k}^{2}  = (1 -  {sin}^{2} A) (1-  {sin}^{2}  B) (1-  {sin}^{2}  C)

     \implies \:  {k}^{2}  =  {cos}^{2}  A \:   {cos \: }^{2} B \:  {cos}^{2}  C

     \implies \: k \:  =  \pm \: cos A \: cos B \: cos C)

    Hence proved

    \displaystyle\textcolor{red}{Please \:  Mark \:  it  \: Brainliest}

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