Question

if 3sinx+4cosx=5,then 4cosx-3sinx =?

Answer 1

$3 \sin( \alpha ) + 4 \cos( \alpha ) = 5 \\ (3 \div 5) \sin( \alpha ) + (4 \div 5)cos \alpha = 1 \\ \cos(53) \sin( \alpha ) + \sin(53) \cos( \alpha ) = 1 \\ \sin(53 + \alpha ) = 1 \\ 53 + \alpha = 90 \\ \alpha = 37 \\ so \\ 4 \cos( \alpha ) - 3 \sin( \alpha ) = ? \\ \alpha = 37 \\ 4(4 \div 5) - 3(3 \div 5) \\ =( 16 - 9) \div 5 \\ = 7 \div 5$
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