How do you sipmify this ?

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How do you sipmify this ?

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Answer 1 · 2018-04-18T12:25:18

$\frac{sin (a + b) - cos (a) sin (b)}{sin (a - b) + cos (a) sin (b)} = 1$ $(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))=1$

Explanation:

We want to simplify

$\frac{sin (a + b) - cos (a) sin (b)}{sin (a - b) + cos (a) sin (b)}$ $(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))$

The angle sum/difference identities

$sin (a + b) = sin (a) cos (b) + cos (a) sin (b)$ $color(red)(sin(a+b)=sin(a)cos(b)+cos(a)sin(b)$
$\Rightarrow sin (a + b) - cos (a) sin (b) = sin (a) cos (b)$ $color(red)(=>sin(a+b)-cos(a)sin(b)=sin(a)cos(b)$
$sin (a - b) = sin (a) cos (b) - cos (a) sin (b)$ $color(blue)(sin(a-b)=sin(a)cos(b)-cos(a)sin(b)$
$\Rightarrow sin (a - b) + cos (a) sin (b) = sin (a) cos (b)$ $color(blue)(=>sin(a-b)+cos(a)sin(b)=sin(a)cos(b)$

Using the identities

$\frac{sin (a + b) - cos (a) sin (b)}{sin (a - b) + cos (a) sin (b)} = \frac{sin (a) cos (b)}{sin (a) cos (b)} = 1$ $(sin(a+b)-cos(a)sin(b))/(sin(a-b)+cos(a)sin(b))= (sin(a)cos(b))/(sin(a)cos(b))=1$

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How do you sipmify this ?

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