Page 55 - Trigonometry

Leaving

= 2 sin( ) cos( − ) + 2 sin( ) cos( )

= 2 sin( ) [cos( − ) + cos( )]

But = 180 − ( + )

Therefore,

cos( ) = cos(180 − ( + ))

= cos(180) cos( + ) + sin(180) sin( + )

= −cos( + )

Leaving

= 2 sin( ) [cos( − ) − cos( + )]

Now

cos( − ) = cos( ) cos( ) + sin( ) sin( )

cos( + ) = cos( ) cos( ) − sin( ) sin( )

When these are subtracted,

cos( − ) − cos( + ) = 2 sin( ) sin( )

Leaving

= 4 sin( ) sin( ) sin( )

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