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.

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

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

$</p><p></p><p>\displaystyle\textcolor{red}{Please \: Mark \: it \: Brainliest}$