Question

If 5 cot θ=3,then find the value of
5 sin θ-3 cos θ/ 4 sin θ+ 3 cos θ

Answer 1

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Given,
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$= > \bf \: 5 \cot( \theta ) = 3 \\ \\ = > \bf \: \cot( \theta ) = \frac{3}{5}$
Now,
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$= > \bf \frac{5 \sin( \theta ) - 3 \cos( \theta ) }{4 \sin( \theta ) + 3 \cos( \theta ) } \\ \\ = > \frac{ \frac{5 \sin( \theta ) - 3 \cos( \theta ) }{ \sin( \theta ) } }{ \frac{4 \sin( \theta ) + 3 \cos( \theta ) }{ \sin( \theta ) } } \\ \\ = > \frac{5( \frac{ \sin( \theta ) }{ \sin( \theta ) } ) -3( \frac{ \cos( \theta ) }{ \sin( \theta ) }) }{4( \frac{ \sin( \theta ) }{ \sin( \theta ) }) + 3( \frac{ \cos( \theta ) }{ \sin( \theta ) }) } \\ \\ = > \frac{5 - 3 \cot( \theta ) }{4 + 3 \cot( \theta ) } \\ \\ = > \frac{5 - 3( \frac{3}{5}) }{4 + 3( \frac{3}{5}) } \\ \\ = > \frac{(5 \times 5) - (3 \times 3)}{(4 \times 5) + (3 \times 3)} \times \frac{5}{5} \\ \\ = > \frac{25 - 9}{20 + 9} \\ \\ = > \bf \underline { \: \frac{16}{29} \: \: }$
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Answer 2

Answer:

16/29

Step-by-step explanation:

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