If 3 tan θ = 4, find the value of $fraction numerator 5 space sin space straight theta minus 3 cosθ over denominator 5 space sinθ plus 2 space cosθ end fraction$
$11 over 26$
$26 over 11$
$12 over 25$
$15 over 28$

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Solution

11 over 26

fraction numerator 5 space sinθ minus 3 space cosθ over denominator 5 space sinθ space plus 2 space cosθ end fraction equals fraction numerator 5 begin display style sinθ over cosθ end style minus 3 begin display style cosθ over cosθ end style over denominator 5 begin display style sinθ over sinθ end style plus 2 begin display style cosθ over cosθ end style end fraction space rightwards double arrow space space fraction numerator 5 space tanθ minus 3 over denominator 5 space tanθ plus 2 end fraction equals fraction numerator 5 cross times begin display style 4 over 3 end style minus 3 over denominator 5 cross times begin display style 4 over 3 end style plus 2 end fraction equals fraction numerator 20 minus 9 over denominator 20 plus 6 end fraction equals 11 over 26

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