Question 1079893
{{{ cos( a - b ) = cos(a)*cos(b) + sin(a)*sin(b) }}}
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In the 3rd quadrant, the cosine is negative
and the sides are 3-4-5, so if
{{{ sin(a) = -3/5 }}}
{{{ cos(a) = -4/5 }}}
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In the 4th quadrant, sine is negative
and cosine is positive.
This sides are 5, 12, 13 , so
{{{ sin(b) = -5/13 }}}
{{{ cos(b) = 12/13 }}}
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{{{ cos( a - b ) = cos(a)*cos(b) + sin(a)*sin(b) }}}
{{{ cos( a - b ) = ( -4/5 )*( 12/13 ) + ( -3/5)*( -5/13 ) }}}
{{{ cos( a - b ) = ( -48/65 ) + 15/65 }}}
{{{ cos( a - b ) = -33/65 }}}
The answer is (C)